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13 students vie for the right t fill up my car weekly during a month. there are 4 weeks in the chosen month. how many different groups are there if ;1) order is not important2) order is important3) there can be repeats

Question

13 students vie for the right t fill up my car weekly during a month. there are 4 weeks in the chosen month. how many different groups are there if ;

1) order is not important

2) order is important

3) there can be repeats

check_circleAnswer
Step 1

Combinations:

It defines the number of possible ways an object can be selected from a group. In combinations, the order of selection does not matter.

Permutations:

It defines the number of possible ways an object can be arranged or ordered. In permutations, order does matters.

Step 2

1) Number of different groups when order is not important:

Here, the value of n is 13 and the value of x is 4. Since order is not important, the combination is appropriate.

The number of different groups when order is not important is obtained as 715, from the calculations given below.

Combination (without repetition)= "C
n!
х(п — х)!
13!
4(13-4)
= 715
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Image Transcriptionclose

Combination (without repetition)= "C n! х(п — х)! 13! 4(13-4) = 715

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Step 3

2) Number of different groups when order is important:

The number of different groups when order is important i...

Permutation (without repetition)=(n-x)!
n!
13!
(13-4
=17,160
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Image Transcriptionclose

Permutation (without repetition)=(n-x)! n! 13! (13-4 =17,160

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