Find the number of ways the letters of the word COMMITTEE can be permuted if the two Ts must be together

All QuestionsCategory: Secondary SchoolFind the number of ways the letters of the word COMMITTEE can be permuted if the two Ts must be together
User Avatar[email protected] asked 10 months ago

Find the number of ways the letters of the word COMMITTEE can be permuted,if the two Ts must be together

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1 Answers
User AvatarStopLearn Team Staff answered 10 months ago

When you want to find the number of permutations of the word COMMITTEE with the condition that the two Ts must be together, you can treat the two Ts as a single entity (let’s call it “T2”) and find the permutations of the resulting seven entities (C, O, M, I, T2, E, and E).
So, you have 7 entities in total. To find the number of permutations, you can use the formula for permutations of a set of distinct objects:
P(n)=n!P(n)=n!
Where:

  • P(n)P(n) is the number of permutations.
  • nn is the total number of entities.

In this case, n=7n=7, so:
P(7)=7!P(7)=7!
Now, you need to account for the fact that the two Es are repeated. To do this, you divide by the permutations of the repeated entities. In this case, you have two Es, so you divide by 2!2! for the permutations of the Es. The formula becomes:
P(7)=7!2!P(7)=2!7!
Now, calculate the number of permutations:
P(7)=7!2!=7×6×5×4×3×2×12×1=2,520P(7)=2!7!=2×17×6×5×4×3×2×1=2,520
So, there are 2,520 ways to permute the letters of the word COMMITTEE with the condition that the two Ts must be together.

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