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# Number of ways in which 25 identical balls can be distributed among Ram, Shyam, Sunder and Ghanshyam such that atleast 1, 2, 3, and 4 balls are given to Ram, Shyam, Sunder and Ghanshyam respectively, is-

^{18}C_{4}^{28}C_{3}^{24}C_{3}^{18}C_{3}

^{18}C_{4}^{28}C_{3}^{24}C_{3}^{18}C_{3}## The correct answer is: ^{18}C_{3}

### First of all select 1 + 2 + 3 + 4 = 10 balls out of 25 identical balls and distribute them as desired. It can happen only in one way. Now let x_{1}, x_{2}, x_{3} and x_{4} balls are given to them respectively.

(where x_{1}, x_{2}, x_{3}, x_{4} 0)

Its now one can get any number of balls

non negative integral solution of

x_{1} + x_{2} + x_{3} + x_{4} = 15

will be the number of ways so

^{15 + 4 –1}C_{4–1} = ^{18}C_{3}

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