Question 1163048: Q1) [] In how many ways can 5 boys and 4 girls be seated in a row so that those of the same gender sit together?
Q3) [] A class has 12 boys and 4 girls. If 3 students are selected at random from the class, what is the probability p that they are all boys?
Q5) [] A student is to answer 8 out of 10 questions on an exam. How many choices has he if he must answer the first 3 questions?
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Q6) [] A class contains 10 men and 20 women of which half the men and half the women have brown
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Depends on whether the order of the boys and the order of the girls matters. In other words, is Billy, Bobby, Brett, Brandon, Bozo a different arrangement than Brandon, Bozo, Billy, Brett, Bobby?
If order doesn't matter, then there are 2 arrangements. Either all 5 boys are first followed by the 4 girls, or all 4 girls are first followed by the boys.
Otherwise, the boys can be arranged in  ways and the girls in  ways. So if the boys come first, there are  ways, and if the girls come first, there are  ways. Altogether, there are  ways.
John
My calculator said it, I believe it, that settles it
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website!
Q1) [] In how many ways can 5 boys and 4 girls be seated in a row so that those of the same gender sit together?
Case 1: BBBBBGGGG
5!4! = (120)(24) = 2880
Case 2: GGGGBBBBB
Same: 2880
Answer: 2880+2880 = 5760
Q3) [] A class has 12 boys and 4 girls. If 3 students are selected at random from the class, what is the probability p that they are all boys?
12 boys CHOOSE 3 12C3 220 11
------------------ = ------ = ------ = ----
16 people CHOOSE 3 16C3 560 28
Q5) [] A student is to answer 8 out of 10 questions on an exam. How many choices has he if he must answer the first 3 questions?
The student has to answer the other 8-3=5 out of the remaining 10-3=7
7 questions CHOOSE 5 = 7C5 = 21
Edwin
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