7 math book 3 physics book are placed at randon on a book shelf. Find the probability that none of the physics book are placed consecutively
Answers
Given : 7 mathematics and 3 physics books are placed on a shelf
To Find : probability that none of the physics book is placed consecutively
Solution:
Mathematics = 7
Physics = 3
Total = 10
10 books can be placed in 10! ways
none of the physics book is placed consecutively
Place 7 books of maths in 7! Ways
Now we have 8 spaces to put 3 physics books
3 physics books can be put in ⁸C₃ = 56 ways
3 boks can be arranged in 3! = 6 ways
Total Ways = 7! . 56 . 6
probability that none of the physics book is placed consecutively
= 7! . 56 . 6 / 10!
= 7! . 56 . 6 / 10 . 9 . 8 . 7 !
= 56 / 10 . 12
= 14 / 30
= 7/15
7/15 is the probability that none of the physics book is placed consecutively
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