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A student group consists of 17 people, 7 of them are girls and

10 of them are boys. How many ways exist to choose a pair of the
same-sex people?

User Faire
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1 Answer

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Answer:

We can solve this problem by using the combination formula, which is:

nCr = n! / (r! * (n - r)!)

where n is the total number of items (people in this case) and r is the number of items we want to select (the group size in this case).

To choose a pair of girls from the 7 girls in the group, we can use the combination formula as follows:

C(7, 2) = 7! / (2! * (7 - 2)!) = 21

Therefore, there are 21 ways to choose a pair of girls from the group.

Similarly, to choose a pair of boys from the 10 boys in the group, we can use the combination formula as follows:

C(10, 2) = 10! / (2! * (10 - 2)!) = 45

Therefore, there are 45 ways to choose a pair of boys from the group.

Since we want to choose a pair of the same-sex people, we can add the number of ways to choose a pair of girls to the number of ways to choose a pair of boys:

21 + 45 = 66

Therefore, there are 66 ways to choose a pair of the same-sex people from the group of 17 people.

User Twinkles
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