# PERMUTATION PRACTICE PROBLEMS WITH ANSWERS

Permutation Practice Problems with Answers :

Here we are going to see some practice questions based on the concept permutation.

## Permutation Practice Problems with Answers

Problem 1 :

Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?

Solution :

Number of letters in the word "SIMPLE"  =  6

All are unique letters.

Number of permutation  = 6P6  =  6!

=  6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1

=  720

Hence total number of permutation is 720.

Problem 2 :

A test consists of 10 multiple choice questions. In how many ways can the test be answered if

(i) Each question has four choices?

(ii) The first four questions have three choices and the remaining have five choices?

(iii) Question number n has n + 1 choices?

Solution :

(i) Each question has four choices?

Number of ways to answer 1st question  =  4

Number of ways to answer 2nd question  =  4

Number of ways to answer 3rd question  =  4

............................

Number of ways  =  4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4

=  410

Hence the total number of ways  =  410

(ii) The first four questions have three choices and the remaining have five choices?

Number of ways to answer 1st question  =  3

Number of ways to answer 2nd question  =  3

Number of ways to answer 3rd question  =  3

Number of ways to answer 4th question  =  3

Number of ways to answer 5th question  =  5

Number of ways to answer 6th question  =  5

..............................

Number of ways  =   3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 5 ⋅ 5 ⋅ 5 ⋅ 5 ⋅ 5 ⋅ 5

=  34⋅ 56

Hence the total number of ways is 34⋅ 56.

(iii) Question number n has n + 1 choices?

Number of ways to answer 1st question  =  2

Number of ways to answer 2nd question  =  3

Number of ways to answer 3rd question  =  4

Number of ways to answer 4th question  =  5

...................

Number of ways to answer 10th question  =  11

Number of ways  =  1  2  3  4  5  6  7  8 ⋅ 9  10  11

=  11!

Hence the total number of ways is 11!. After having gone through the stuff given above, we hope that the students would have understood, how to solve problems on permutations.

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