Question

In how many ways can a boy invite his 5 friends to a party so that at least three join the party?

Answer 1

Number of friends n = 5.

At least three join the party

∴ r ≥ 3

∴ the number of ways in which a boy can invite 5 friends so that at least three join the party

= ⁵C₃ + ⁵C₄ + ⁵C₅

= `(5!)/(3!2!) + (5!)/(4!1!) + (5!)/(5!0!)`

= `(5 xx 4 xx 3!)/(1 xx 2 xx 3!) + (5 xx 4!)/(4!) + 1`

= 10 + 5 + 1

= 16.