Total number of ways in which 15 identical blankets can be distributed among 4 persons so that each of them get atleast two blankets equal to ?

Asked by prabhakar p | 29th Apr, 2013, 02:38: PM

Expert Answer:

Let x1, x2, x3 and xbe the number of blankets possessed by each person.

The total number of blankets is 15. So, x1+ x2+ x3 + x4 = 15.

Now we also know that all the persons involved get 2 blankets each. Therefore, first let us distribute 2 blankets to each person.

Then we will have 15 - 2 x 4 = 7 blankets left. It is these 7 blankets that we have to now distribute amongst 4 persons because 2 blankets have already been given to each of the 4 persons.

The number of ways in which n objects can be distributed in r different groups is n+r-1Cr-1 if the number of objects per group can be zero.

Therefore, the number of ways in which 7 blankets can be distributed amongst 4 persons is 7 + 4 - 1C4-1 = 10C3.
 
Note: Please cross check, the options that you mentioned are not appropriate.

Answered by  | 30th Apr, 2013, 10:07: AM

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