In how many ways can a committee of one or more than one member from 10 can be formed?A.210210B.102 102 C.210−1210−1D.102−1
Question
In how many ways can a committee of one or more than one member from 10 can be formed?
A. 210
B. 102
C. 210−1
D. 102−1
Solution
To find the number of ways a committee can be formed from a group of 10 members, we need to consider all possible combinations.
Step 1: Determine the number of ways to form a committee with one member. Since there are 10 members in total, there are 10 ways to choose one member.
Step 2: Determine the number of ways to form a committee with more than one member. This can be done by considering all possible group sizes.
For a group size of 2, there are 10 choose 2 ways to form a committee. This can be calculated using the formula: C(n, r) = n! / (r!(n-r)!), where n is the total number of members and r is the group size. In this case, n = 10 and r = 2. Plugging in the values, we get C(10, 2) = 10! / (2!(10-2)!) = 45.
For a group size of 3, there are 10 choose 3 ways to form a committee. Using the same formula, we get C(10, 3) = 10! / (3!(10-3)!) = 120.
Continuing this pattern, we can calculate the number of ways to form a committee for group sizes of 4, 5, 6, 7, 8, 9, and 10.
Step 3: Add up the number of ways to form a committee for each group size.
In this case, the answer is not explicitly given in the options. However, we can calculate the total number of ways by summing up the individual counts for each group size.
So, the correct answer is not provided in the given options.
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