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Bunuel
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A committee of 5 is to be selected from among 5 boys and 6 girls. I ho 26 Oct 2023, 07:01
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35% (medium)

Question Stats:

74% (01:56) correct 26% (02:28) wrong based on 72 sessions

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A committee of 5 is to be selected from among 5 boys and 6 girls. In how many ways can this be done if the committee is to consist of at-least one girl?

(A) 105
(B) 225
(C) 230
(D) 455
(E) 461
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A committee of 5 is to be selected from among 5 boys and 6 girls. I ho 26 Oct 2023, 07:06
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Ans is 461 which is not in the option.
11c5-5c5

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A committee of 5 is to be selected from among 5 boys and 6 girls. I ho 30 Oct 2023, 07:50
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Ways of selecting at least one girl= Total no of ways - No of ways with no girl

From 11, selecting a committee of 5= 11C5
No girl means there are only boys= committee of 5 from 5 boys= 5C5

-> 11C5-5C5 -> 462-1
461 (answer)
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A committee of 5 is to be selected from among 5 boys and 6 girls. I ho 30 Oct 2023, 08:04
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To find the number of ways to select a committee of 5 members from 5 boys and 6 girls, such that the committee must consist of at least one girl, you can use the principle of inclusion-exclusion.

First, find the total number of ways to select a committee of 5 members without any restrictions, which is the combination of 5 people from the total of 11 (5 boys + 6 girls):

C(11, 5) = 11! / (5!(11-5)!) = 462 ways

Next, calculate the number of ways to select a committee of 5 members that consists only of boys:

C(5, 5) = 1 way

Now, we can calculate the number of ways to select a committee that includes at least one girl using the principle of inclusion-exclusion. Subtract the number of committees that consist only of boys from the total number of committees:

462 (total) - 1 (only boys) = 461 ways

So, there are 461 ways to select a committee of 5 members that includes at least one girl.
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