KVPY 2020-21 SA Exam Previous Papers

Question : 13 of 80

Marks: +1, -0

The number of permutations of the letters

a_{1}, a_{2}, a_{3}, a_{4}, a_{5}

in which the first letter

a_{1}

does not occupy the first position (from the left) and the second letter

a_{2}

does not occupy the second position (from the left) is

Solution:

No. of ways

=5 !(1-{1}/{1 !}+{1}/{2 !}-{1}/{3 !}+{1}/{4 !}-{1}/{5 !})

+3 C_{1}(1-{1}/{1 !}+{1}/{2 !}-{1}/{3 !}+{1}/{4 !})

+3 C_{2}(1-{1}/{1 !}+{1}/{2 !}-{1}/{3 !})+3 C_{3} \.1

= 44 + 27 + 6 + 1 = 78

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