There are 10 men and 11 women in an office. In how many ways can a team of 5 men and 5 women be selected?

To solve this problem, we will use the concept of combinations from combinatorics.

Step 1: Selecting 5 men out of 10 The number of ways to select 5 men out of 10 is given by the combination formula C(n, r) = n! / [(n-r)!r!], where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.

So, the number of ways to select 5 men out of 10 is C(10, 5) = 10! / [(10-5)!5!] = 252 ways.

Step 2: Selecting 5 women out of 11 Similarly, the number of ways to select 5 women out of 11 is given by the combination formula C(n, r) = n! / [(n-r)!r!].

So, the number of ways to select 5 women out of 11 is C(11, 5) = 11! / [(11-5)!5!] = 462 ways.

Step 3: Combining the selections Since the selections of men and women are independent events, we multiply the number of ways to get the total number of ways to select a team of 5 men and 5 women.

So, the total number of ways = 252 ways (to select men) * 462 ways (to select women) = 116424 ways.

Therefore, a team of 5 men and 5 women can be selected in 116424 ways.