(Q). In how many ways 15 students can be arranged in a row ?
Sol:- 15 students can be arranged in a row in 15! ways Answer
(Q). In how many ways 8 prizes from 1ˢᵗ to 8ᵗʰ can be given to a group of 8 students that includes 4 boys & 4 girls. Here a student can get only 1 prize ?
Sol:- Here we are to arrange 8 distinct prizes at 8 distinct places (8 distinct students).
which can be done in 8! ways Answer
In this question the sentence ‘4 boys & 4 girls’ is irrelevant only thing that matters is 8 students i.e. 8 different places.
(Q). In how many ways 12 boys and 10 girls can be arranged in a straight line such that all the girls and all the boys are together ?
Sol:-
12 boys in themselves can be arranged in 12! ways.
10 girls in themselves can be arranged in 10! ways.
now these two bunches can be arranged in 2! ways.
Hence total number of ways = 12!.10!.2! Answer
(Q). In how many ways 4 pens can be given to 8 students if each student can get any number of prizes ?
Sol:- 1ˢᵗ pen can be given to any student.
Hence 1ˢᵗ pen can be given in 8 ways.
2ⁿᵈ pen can be given to any student.
Hence 2ⁿᵈ pen can be given in 8 ways
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Similarly, 4ᵗʰ pen can be given in 8 ways
Hence total number of ways = 8×8×8×8
= 8⁴ Answer