Final answer:
To form a committee of 3 from 11 names where each member has a different role, we use permutations. There are 990 ways to form the committee, which is calculated using the permutation formula P(n, k) = n! / (n - k)!
option A is correct answer.
Step-by-step explanation:
The student's question involves determining in how many ways a committee of 3 can be formed from 11 names on a ballot, where each person on the committee will have a different responsibility.
This is a permutation problem because the order matters, as each committee member will have a different responsibility. To solve this, we use the permutation formula P(n, k) = n! / (n - k)!, where n is the total number of items to choose from, and k is the number of items to choose. Here, n is 11 and k is 3.
Calculate the factorial of n (11! = 11 × 10 × 9 × ... × 1).
Calculate the factorial of n - k (11 - 3)! = 8! = 8 × 7 × ... × 1).
Divide the factorial of n by the factorial of n - k (11! / 8! = 11 × 10 × 9 / 8 × 7 × ... × 1).
The calculation simplifies to 11 × 10 × 9, since the 8! terms cancel out. Multiplying these together gives us 990.
Therefore, there are 990 ways to form the committee. The correct answer to the student's question is a. 990 ways.