ese pos as vertices? 5b 15. From a deck of 52 playing cards, how 16. From a deck

Question

ese pos as vertices? 5b 15. From a deck of 52 playing cards, how 16. From a deck of 52 p many different 5-card hands can have 5 cards of the same suit? 5148 many different 4-card hands can have each card from a different suit? 28,561 ag contains 4 red, 6 white, and 9 blue marbles. How many ways can 5 marbles be selected to meet the following conditions? 17. All the marbles are white. 6 19. All the marbles are red. o 18. All the marbles are blue. 126 810 20. Two are red, 2 are white, and 1 is blue. I. Two must be blue. 4320 22. Two are 1 color and 3 are another color. 280 From a group of 8 men and 10 women, a committee of 5 is to be formed. How many Committees can be formed if the committee is to be comprised as follows? 23. All are men. 56 25 24. There are 3 men and 2 women. 2520 26. All are women. 252 There is 1 man and 4 women. 1680

Explanation / Answer

#15.
5 cards from 13 suit cards can be selected in 13C5 ways and there are 4 suits hence total possible ways are

4C1 * 13C5 = 5148

#16.
1 card from each suit can be selected in

13C1*13C1*13C1*13C1 = 13^4 = 28561

#17.
5 white marbles can be selected in 6C5 = 6 ways

#18.
5 blue marbles can be selected in 9C5 ways = 126

#19.
There are only 4 red marbles, we cannot select 5 red marbles. Hence 0

#20.
Two red in 4C2, two white in 6C2 and 1 blue in 9C1 ways

Hence 4C2*6C2*9C1 = 810

#21.
2 blue marbles selected in 9C2 and other 3 can be selected in 10C3 ways.

Hence 9C2*10C3 = 4320

#22.
Required combinations are

4C2*6C3 + 4C2*9C3 + 6C2*9C3 + 6C2*4C3 + 9C2*4C3 + 9C2*6C3 = 2808

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