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

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

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.

Concept: Properties of Combinations

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

The number of ways of inviting at least three friends from 5 friends

= `""^5"C"_3 + ""^5"C"_4 + ""^5"C"_5`

= `(5!)/((5 - 3)!3!) + (5!)/((5 - 4)!4!) + 1`

= `(5 xx 4)/(2xx 1) + 5  + 1`

= 10 + 5 + 1
= 16

Concept: Properties of Combinations

  Is there an error in this question or solution?