Latest Book Aptitude Question SOLUTION: In how many ways 12 different books can be distributed equally among 4 persons? (a)195 (b)154 (c)210 (d)256

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(#M40035575) BOOK Numerical Ability question Permutationand Combination Keep an EYE

In how many ways 12 different books can be distributed equally among 4 persons?
(a)195
(b)154
(c)210
(d)256

Asked In Book indrajeet yadav (10 years ago)

Unsolved Read Solution (3)

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Read Solution (3) :

Subrata Patra  (10 years ago)

We assume that the all are distinct.
Also the books have to be evenly distributed i.e. 3 books per person.
For the first person we have to select 3 from 12, so no. of combinations = 12C3
After this 9 books are left.
For the second person we have to select 3 from 9, so no. of combinations = 9C3
Similarly for the third person it is 6C3
and for the fourth person it is 3C3.
So the required no. of ways the books can be evenly distributed is 12C3 x 9C3 x 6C3 x 3C3
= 220 x 84 x 20 x 1 = 369600.
Note that the sequence or position of distribution does not matter, so it is not permutation.

Is this solution Helpfull? Yes (2) | No (1)  

NAGENDRA P  (10 years ago)

12C3*9C3*6C3*3C3=369600

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AMIT YADAV  (10 years ago)

Here we can clearly recognize that 12 Books have to be distributed among 4 persons equally.
so 12 books can be distributed to 3-3 persons.
therefore, it is solved through combination.
4 books to 1st 3 persons = 12C3
4 Books to 2nd 3 persons = 9C3
4 books to 3rd 3 persons = 6C3
4 books to 4th 3 persons = 3C3
Hence, distribution to 4 persons equally = 12C3 * 9C3 * 6C3 * 3C3 =220 * 84 * 20* 1 = 369600.

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