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Find the total number of ways in which 20 balls can be put in 5 boxes so that the first box contains just one ball. 

(a) 205 

(b) 520 

(c) 20 × 419 

(d) 420

1 Answer

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(c) 20 × 419

One ball can be put in first box in 20 ways because we can put any one of the twenty balls in the first box. Now, remaining 19 balls are to be put into remaining 4 boxes. This can be done in 419 ways, because there are 4 choices for each ball. Hence, the required number of ways = 20 × 419.

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