Math, asked by arifasherin2971, 11 months ago

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

Answered by amitnrw
1

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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