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# in a club with 9 male and 11 female members, how many 5 memeber committees can be chosen that have..

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in a club with 9 male and 11 female members, how many 5 memeber committees can be chosen that have..

A.) at least 4 women?

B.)no more than 2 men?

Nov 9, 2014

#1
+394
+13

ncr(20,5)= 15504 ----Total number of ways to select 5 of twenty.

-------------------------

A.) Solution for at least 4 women

ncr(11,5)*ncr(9,0) = 462 Number of ways to select 5 of 11 females and select 0 of 9 males

ncr(11,4)*ncr(9,1) = 2970 Number of ways to select 4 of 11 females and select 1 of 9 males

Sum of combinations total = 3432. So there are 3432 ways to select this group of 5 where 4 or more are women.

(3432/15504 = 22.1%) Incidental probability of this occurring.

-------------------------

B.) Solution for no more than 2 men.

ncr(11,5)*ncr(9,0)= 462 Number of ways to select 5 of 11 females and select 0 of 9 males.

ncr(11,4)*ncr(9,1) = 2970 Number of ways to select 4 of 11 females and select 1 of 9 males.

ncr(11,3)*ncr(9,2) = 5940 Number of ways to select 3 of 11 females and select 2 of 9 males.

Sum of combinations total = 9372. So there are 9372 ways to select this group of 5 where 2 or less are men.

(9372/15504 = 60.4%) Incidental probability of this occurring.

I doubled checked this, but Melody, CPhill, or Alan should verify the answers.

PS This assumes males are men and females are women. My dad says it is not easy to tell any more. So far, I don’t seem to have a problem. LOL

~7UP~

Nov 9, 2014

#1
+394
+13

ncr(20,5)= 15504 ----Total number of ways to select 5 of twenty.

-------------------------

A.) Solution for at least 4 women

ncr(11,5)*ncr(9,0) = 462 Number of ways to select 5 of 11 females and select 0 of 9 males

ncr(11,4)*ncr(9,1) = 2970 Number of ways to select 4 of 11 females and select 1 of 9 males

Sum of combinations total = 3432. So there are 3432 ways to select this group of 5 where 4 or more are women.

(3432/15504 = 22.1%) Incidental probability of this occurring.

-------------------------

B.) Solution for no more than 2 men.

ncr(11,5)*ncr(9,0)= 462 Number of ways to select 5 of 11 females and select 0 of 9 males.

ncr(11,4)*ncr(9,1) = 2970 Number of ways to select 4 of 11 females and select 1 of 9 males.

ncr(11,3)*ncr(9,2) = 5940 Number of ways to select 3 of 11 females and select 2 of 9 males.

Sum of combinations total = 9372. So there are 9372 ways to select this group of 5 where 2 or less are men.

(9372/15504 = 60.4%) Incidental probability of this occurring.

I doubled checked this, but Melody, CPhill, or Alan should verify the answers.

PS This assumes males are men and females are women. My dad says it is not easy to tell any more. So far, I don’t seem to have a problem. LOL

~7UP~

SevenUP Nov 9, 2014
#2
+94607
+5

I didn't run the numbers 7UP, but it looks good....well done !!!

Nov 9, 2014
#3
+394
+8

Thank You CPhill. I have learned a lot from you, Melody and Alan!

Nov 9, 2014
#4
+94607
+3

Thanks for those kind words......I'll recommend that Melody use your answer in her "Daily Wrap"....

Nov 9, 2014