Question

Answer the following question using arrangements with​ repetition, permutations, or combinations. Be sure to explain why...

Answer the following question using arrangements with​ repetition, permutations, or combinations. Be sure to explain why the particular counting technique applies to the problem.

How many different eighteight​-digitdigit passwords can be formed from the numbers zero to eightnumbers zero to eight if repetition is not​ allowed?

Determine the appropriate counting technique. Choose the correct answer below.

A. Permutations should be used because we make selections from a group of choices.

B. Permutations should be used because no item may be selected more than once and the order matters.

C. ​Combinations, because no item may be selected more than once and the order does not matter.

D. Arrangements with repetition should be used because we make selections from a group of choices.

E. Arrangements with repetition should be used because no item may be selected more than once and the order matters.

Calculate how many different passwords are possible.

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Answer #1

Ans:

Option B is correct.

Permutations should be used because no item may be selected more than once and the order matters.

we have digits 0,1,2,3,4,5,6,7,8,9

First place can be filled with 9 choices,second place can be filled with 8 choices,third place can be filled with 7 choices and so on...

Number of different passwords are possible=9*8*7*6*5*4*3*2=362880

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