In how many ways can a subset of 7 elements be chosen from a set containing 10 elements

Answer 1

To find the number of ways to choose a subset of 7 elements from a set containing 10 elements, we can use the combination formula.

The formula for the number of combinations is given by:

C(n, k) = n! / (k! * (n-k)!)

Where n is the total number of elements in the set and k is the number of elements we want to choose for the subset.

In this case, n = 10 and k = 7.

Using the formula, we can calculate:

C(10, 7) = 10! / (7! * (10-7)!)
= 10! / (7! * 3!)

Simplifying further:

10! = 10 * 9 * 8 * 7!
3! = 3 * 2 * 1
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1

C(10, 7) = (10 * 9 * 8 * 7!)/(7! * 3 * 2 * 1)
= (10 * 9 * 8)/(3 * 2 * 1)
= 10 * 3
= 30

Therefore, there are 30 ways to choose a subset of 7 elements from a set containing 10 elements.