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-> SOLUTION: Help! A woman has 11 close friends. In how many ways can she invite 5 of them for dinner, if there are 2 who are not in good talking terms and so both can not be at the dinner, b Log On
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Lisa has 5 friends in how many ways can she invite one or more of them [#permalink]
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Lisa has 5 friends in how many ways can she invite one or more of them at a dinner party?(A) 63(B) 32(C) 31(D) 25
(E) 24
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Re: Lisa has 5 friends in how many ways can she invite one or more of them [#permalink]
Bunuel wrote:
Lisa has 5 friends in how many ways can she invite one or more of them at a dinner party?(A) 63(B) 32(C) 31(D) 25
(E) 24
Lisa can invite either \(1\) or \(2\) or \(3\) or \(4\) or all \(5 \) of them to the party:Hence \(5c1+ 5c2+5c3+5c4+5c5 = 5+10+10+5+1= 31\)Ans-CHope it's clear. _________________
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Re: Lisa has 5 friends in how many ways can she invite one or more of them [#permalink]
Bunuel wrote:
Lisa has 5 friends in how many ways can she invite one or more of them at a dinner party?(A) 63(B) 32(C) 31(D) 25
(E) 24
Solution:Lisa can invite exactly r (where r = 1, 2, 3, 4, or 5) friends in 5Cr ways. Therefore, Lisa can invite one or more of her 5 friends in a total of 5C1 + 5C2 + 5C3 + 5C4 + 5C5 = 2^5 - 5C0 = 32 - 1 = 31 ways.
Alternate Solution:
If we think of Lisa’s five friends as a set, then the number of ways she can invite her friends to the dinner party is in one to one correspondence with the subsets of the set of friends. Recall that a set with five elements has 2^5 = 32 subsets. One of these subsets is the empty set, which corresponds to inviting zero friends. Taking away the empty set, we see that there are 32 - 1 = 31 ways Lisa can invite one or more of her friends.Answer: C
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Re: Lisa has 5 friends in how many ways can she invite one or more of them [#permalink]
Given• Lisa has 5 friends.
To find
• The number of ways Lisa can invite one or more of her friends at a dinner party.Approach and Working out:
Method 1
- • Total ways = 5C1 +5c2 +5c3+5c4 +5c5
Correct Answer: Option C
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Re: Lisa has 5 friends in how many ways can she invite one or more of them [#permalink]
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Re: Lisa has 5 friends in how many ways can she invite one or more of them [#permalink]
27 Apr 2022, 00:38