Question

# Dropdi has 5 friends. In how many ways can she invite one or more of them to a dinner?

A
31
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B
55
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C
13
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D
25
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Solution

## The correct option is A 31 She may invite one or more friends by selecting either 1 or 2 or 3 or 4 or 5 friends out of 5 friends. ∴ 1 friend can be selected out of 5 in 5C1 ways 2 friend can be selected out of 5 in 5C2 ways 3 friend can be selected out of 5 in 5C3 ways 4 friend can be selected out of 5 in 5C4 ways 5 friend can be selected out of 5 in 5C5 ways Hence the required number of ways =5C1+5C2+5C3+5C4+5C5=5+10+10+5+1=31 Alternatively :5C1+5C2+5C3+5C4+5C5=25−1=31 Since, nC1+nC2+nC3+....+Cn=2n−1

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