Question

Assume that you have 4 dimes and 2 quarters (all distinct), and you select 3 coins. (1) In how many ways can the selection be made? (2) In how many ways can the selection be made if all the coins are dimes? (3) In how many ways can the selection be made if you select 2 dimes and 1 quarter? (4) In how many ways can the selection be made so that at least 2 coins are dimes?

          Assume that you have 4 dimes and 2 quarters (all distinct), and you select 3 coins.
(1) In how many ways can the selection be made?       
(2) In how many ways can the selection be made if all the coins are dimes?       
(3) In how many ways can the selection be made if you select 2 dimes and 1 quarter?       
(4) In how many ways can the selection be made so that at least 2 coins are dimes?
        
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Added by Kayla C.

Probability with Applications in Engineering, Science, and Technology
Probability with Applications in Engineering, Science, and Technology
Matthew A. Carlton • Jay L. Devore 2nd Edition
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Assume that you have 4 dimes and 2 quarters (all distinct), and you select 3 coins. (1) In how many ways can the selection be made? (2) In how many ways can the selection be made if all the coins are dimes? (3) In how many ways can the selection be made if you select 2 dimes and 1 quarter? (4) In how many ways can the selection be made so that at least 2 coins are dimes?
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Transcript

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00:01 In this question, we have 4 dimes and 2 quarters and they are all distinct.
00:07 Total number of coins is 6 and you select 3 coins.
00:12 In part 1, want to find the number of ways the selections can be made.
00:18 Take note that the 3 coins are selected without replacement and that the order of selection is not important.
00:32 This will be using combination.
00:37 There is n -chus -r.
00:39 So number of ways the selection can be made without any restriction, that will be from the six coins we choose three.
00:48 And that's 20 ways.
00:51 Number of ways the selection can be made if all the coins are dimes.
00:55 So from the four times, we're just going to choose three.
00:59 And so the answer is four...
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