A bag contains 4 red marbles, 3 blue marbles, and 5 purple marbles....

A bag contains 4 red marbles, 3 blue marbles, and 5 purple marbles. A sample of 4 marbles is taken out of the bag. In how many ways can at least 3 marbles be purple?


You keep your socks loose in a drawer. You have 6 black socks, 8 white socks, and 4 navy blue socks. This morning you were very tired and didn't look as you grabbed two socks out of the drawer and put them on. In how many ways can you grab two socks of the same color?


A bridge hand is made up of 13 cards. In how many ways can a bridge hand contain exactly 3 spades, 4 diamonds, and 2 clubs?

crutch said:

A bag contains 4 red marbles, 3 blue marbles, and 5 purple marbles. A sample of 4 marbles is taken out of the bag. In how many ways can at least 3 marbles be purple?


You keep your socks loose in a drawer. You have 6 black socks, 8 white socks, and 4 navy blue socks. This morning you were very tired and didn't look as you grabbed two socks out of the drawer and put them on. In how many ways can you grab two socks of the same color?


A bridge hand is made up of 13 cards. In how many ways can a bridge hand contain exactly 3 spades, 4 diamonds, and 2 clubs?

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crutch said:

1. A bag contains 4 red marbles, 3 blue marbles, and 5 purple marbles. A sample of 4 marbles is taken out of the bag. In how many ways can at least 3 marbles be purple?

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Are you assuming that marbles of the same color are indistiguishable, so "a purple, a red, and two more purples" is regarded as exactly the same as "three purples and a red"?

crutch said:

2. You keep your socks loose in a drawer. You have 6 black socks, 8 white socks, and 4 navy blue socks. This morning you were very tired and didn't look as you grabbed two socks out of the drawer and put them on. In how many ways can you grab two socks of the same color?

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You have three colors. Where are you getting stuck?

crutch said:

3. A bridge hand is made up of 13 cards. In how many ways can a bridge hand contain exactly 3 spades, 4 diamonds, and 2 clubs?

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They have specified the suits of 3 + 4 + 2 = 9 of the thirteen cards. In how many ways can you choose three spades (of the thirteen available)? How many ways can you pick the other specified cards? Since there are three cards remaining and they've specified "exactly", what is left for you to choose?

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