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Question 28

Mathematics Permutation and Combination Medium

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

(A) \(10 \times 3^{10}\)

(B) \(20 \times 4^{19}\)

(C) \(30 \times 2^{9}\)

(D) \(25 \times 7^{5}\)

✓ Correct Answer: Option B Verified Solution

The balls are distinct.

Choose the one ball that goes into the first box: \(\binom{20}{1} = 20\) ways.
Each of the remaining 19 balls can go into any of the other 4 boxes: \(4^{19}\) ways.

Total = \(20 \times 4^{19}\)

Answer: (B)

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