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-

  1. 18C4
  2. 28C3
  3. 24C3
  4. 18C3

The correct answer is: 18C3

    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 x1, x2, x3 and x4 balls are given to them respectively.
    (where x1, x2, x3, x4 greater or equal than 0)
    Its now one can get any number of balls
    therefore non negative integral solution of
    x1 + x2 + x3 + x4 = 15
    will be the number of ways so
    15 + 4 –1C4–1 = 18C3

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