Mẹo How many words can be formed from the letters of the word TRIANGLE which begin with T and end with e ?
Thủ Thuật về How many words can be formed from the letters of the word TRIANGLE which begin with T and end with e Chi Tiết
Hoàng Tiến Dũng đang tìm kiếm từ khóa How many words can be formed from the letters of the word TRIANGLE which begin with T and end with e được Cập Nhật vào lúc : 2022-09-20 00:50:16 . Với phương châm chia sẻ Bí kíp Hướng dẫn trong nội dung bài viết một cách Chi Tiết 2022. Nếu sau khi Read Post vẫn ko hiểu thì hoàn toàn có thể lại Comments ở cuối bài để Tác giả lý giải và hướng dẫn lại nha.Problem 1
The letters of the word TRIANGLE are arranged random. Find the probability and odds that the word so formed (i) starts with T (ii) ends with R (iii) starts with T and ends with R.
Nội dung chính- Problem 1 For Event A For Event B For Event C How many words can be formed starting with T and ending with E from the word TRIANGLE without repetition?What word starts with T and ends with E?How many words can be formed using the letters of the word TRIANGLE so that t/r i are always together?How many different words can you make with TRIANGLE?
Solution
In the word TRIANGLE
Number of Letters/Characters
= 8
T, R, I, A, N, G, L, E
⇒ nL = 8
Experiment :
Forming a word using the 8 letters
Total Number of Possible Choices
= Number of words that can be formed using the 8 letters
When there are large factorial values, using the factorial form would reduce the burden of calculations
Let
A : the sự kiện of the word formed starting with T
B : the sự kiện of the word formed ending with R
C : the sự kiện of the word formed starting with T and ending with R
For Event A
In forming words that start with T,
Number of letters fixed, each in its own place
= 1
⇒ nFL = 1
After fixing the specified letters in their respective places
Number of letters remaining
= Total Number of letters − Number of letters fixed in specific places
⇒ nRL = nL − nFL = 8 − 1 = 7Number of places remaining to be filled
= Total Number of Places − Number of letters fixed in specific places
⇒ nRP = nP − nFL = 8 − 1 = 7Number of Favorable Choices
= Number of words that can be formed using the letters of the word TRIANGLE fixing T in the first place
= Number of ways in which the specified letters can be fixed each in its own place × Number of ways in which the remaining letters can be arranged in the remaining places
= nFLPnFL × nRLPnRP
= 1 × nRLPnRP
= nRLPnRP
Probability that the word formed using all the letters of the word TRIANGLE starts with T
⇒ Probability of occurrence of Event A
= Number of Favorable Choices for the Event Total Number of Possible Choices for the ExperimentOdds
Number of Unfavorable Choices
= Total Number of possible choices − Number of Favorable choices
⇒ mAc = n − mA = 8! − 7! = 8 × 7! − 7! = (8 − 1) × 7! = 7 × 7!in favor
Odds in Favor of the word formed starting with T
⇒ Odds in Favor of Event A
= Number of Favorable Choices : Number of Unfavorable Choices
= mA : mAc
= 7! : 7 × 7!
= 1 : 7
against
Odds against the word formed starting with T
⇒ Odds against Event A
= Number of Unfavorable Choices : Number of Favorable Choices
= mAc : mA
= 7 × 7! : 7!
= 7 : 1
For Event B
In forming words that ends with R
Number of letters fixed, each in its own place
= 1
⇒ nFL = 1
After fixing the specified letters in their respective places
Number of letters remaining
= Total Number of letters − Number of letters fixed in specific places
⇒ nRL = nL − nFL = 8 − 1 = 7Number of places remaining to be filled
= Total Number of Places − Number of letters fixed in specific places
⇒ nRP = nP − nFL = 8 − 1 = 7Number of Favorable Choices
= Number of words that can be formed using the letters of the word TRIANGLE fixing R in the last place
= Number of ways in which the specified letters are fixed each in its own place × Number of ways in which the remaining letters are arranged in the remaining places
= nFLPnFL × nRLPnRP
= 1 × nRLPnRP
= nRLPnRP
Probability that the word formed using all the letters of the word TRIANGLE ends with R
⇒ Probability of occurrence of Event B
= Number of Favorable Choices for the Event Total Number of Possible Choices for the ExperimentFor Event C
In forming words that start with T and end with R,
Number of letters fixed, each in its own place
= 2
⇒ nFL = 2
After fixing the specified letters in their respective places
Number of letters remaining
= Total Number of letters − Number of letters fixed in specific places
⇒ nRL = nL − nFL = 8 − 2 = 6Number of places remaining to be filled
= Total Number of Places − Number of letters fixed in specific places
⇒ nRP = nP − nFL = 8 − 2 = 6Number of Favorable Choices
= Number of words that can be formed using the letters of the word TRIANGLE fixing T in the first place and R in the last place
= Number of ways in which the specified letters are fixed each in its own place × Number of ways in which the remaining letters are arranged in the remaining places
= nFLPnFL × nRLPnRP
= 1 × nRLPnRP
= nRLPnRP
Probability that the word formed using all the letters of the word TRIANGLE starts with T and end with R
⇒ Probability of occurrence of Event C
= Number of Favorable Choices for the Event Total Number of Possible Choices for the ExperimentOdds
Number of Unfavorable Choices
= Total Number of possible choices − Number of Favorable choices
⇒ mAc = n − mA = 8! − 6! = 8 × 7 × 6! − 7! = 56 × 6! − 7! = (56 − 1) × 6! = 55 × 6!in favor
Odds in Favor of the word formed starting with T and ending with R
⇒ Odds in Favor of Event C
= Number of Favorable Choices : Number of Unfavorable Choices
= mC : mCc
= 6! : 55 × 6!
= 1 : 55
against
Odds against the word formed starting with T and ending with R
⇒ Odds against Event C
= Number of Unfavorable Choices : Number of Favorable Choices
= mCc : mC
= 55 × 6! : 6!
= 55 : 1
How many words can be formed starting with T and ending with E from the word TRIANGLE without repetition?
Therefore, the total number of words formed from the word TRIANGLE is 40,320 out of which 720 words start with T and end with E.What word starts with T and ends with E?
5-Letter Words Starting with T and Ending in E List. table.. tache.. targe.. tarre.. tasse.. taste.. tatie.. taube..How many words can be formed using the letters of the word TRIANGLE so that t/r i are always together?
= 40320. We have given the word TRIANGLE.How many different words can you make with TRIANGLE?
349 words can be made from the letters in the word triangle. Tải thêm tài liệu liên quan đến nội dung bài viết How many words can be formed from the letters of the word TRIANGLE which begin with T and end with e