How many ways can a foursome of two men and two women be selected from 10 men and 12 women to sit at a table in a restaurant?
To solve this problem, we need to use the combination formula:
nCr = n! / r!(n-r)!
where n is the total number of items, r is the number of items we want to select, and ! means factorial (the product of all positive integers up to that number).
In this case, we want to select 2 men out of 10 and 2 women out of 12, and arrange them at a table. So we have:
Number of ways to select 2 men out of 10: 10C2 = 10! / 2!(10-2)! = 45
Number of ways to select 2 women out of 12: 12C2 = 12! / 2!(12-2)! = 66
Number of ways to arrange the foursome at the table: 4! = 24 (since there are 4 people and 4 seats, and each person can sit in any of the 4 seats)
Therefore, the total number of ways to select and arrange the foursome is:
45 * 66 * 24 = 71,280
So there are 71,280 ways to select a foursome of two men and two women from 10 men and 12 women to sit at a table in a restaurant.