The number of subsets of set {a, B, C} containing element a is

The number of subsets of set {a, B, C} containing element a is

Four: {a}, {a, B}, {a, C}, {a, B, C}

For a set with n elements, 1) the number of subsets with only one element 2) the number of subsets with only two elements 3) the number of subsets with only three elements
The solution of set with n elements
1) The number of subsets with only one element
2) The number of subsets with only two elements
3) The number of subsets with only three elements
4) The number of subsets containing only m elements

A set of n elements
1) The number of subsets with only one element: C (n, 1) = n
2) The number of subsets with only two elements: C (n, 2) = n (n-1) / 2
3) The number of subsets with only three elements: C (n, 3) = n (n-1) (n-2) / 6
4) The number of subsets with m elements: C (n, m) = n * (n-1) * (n-2)... * (n-m + 1) / m * (m-1) * (m-2)... * 1

Given a = {1,2,3,4,5,6,}, B = {4,5,6,7,8}, set s is a subset of a, and s ∩ B ≠ &;;, find the number of S

Because s is a subset of a, and s ∩ B ≠ Φ, it means that s must contain elements 4, 5, 6 (one, two or three), so the number of S is (C (3,1) + C (3,2) + C (3,3)) * 2 ^ 3 = 7 * 8 = 56