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