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A football team of 11 members is to be selected from 13 girls. In how many ways ...

Question

A football team of 11 members is to be selected from 13 girls. In how many ways can this be done if any player can play any wing?

A)
156
B)
71
C)
143
D)
78

Explanation:

In this question, we are asked to find the number of possible ways to select a football team of 11 members from 13 girls. Since any player can play any wing, we only need to focus on the number of combinations that can be formed.

To find the number of ways to select 11 members from a group of 13, we can use the combination formula, which is:

$$C(n, r) = \frac{n!}{r!(n - r)!}$$

where n is the total number of items (in this case, the girls) and r is the number of items to be chosen (the team members).

Plugging in the values, we get:

$$C(13, 11) = \frac{13!}{11!(13 - 11)!} = \frac{13!}{11!2!}$$

Let's simplify the factorial expressions:

$$\frac{13 \times 12 \times 11!}{11! \times 2 \times 1} = \frac{13 \times 12}{2} = 13 \times 6$$

Now, we can multiply the numbers:

$$13 \times 6 = 78$$

So, there are 78 different ways to select a football team of 11 members from 13 girls, and the correct option is Option D.