Find the total number of ways to put $20$ balls into $5$ boxes so that the firs…

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

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Choose which ball goes to Box 1: $20$ ways. Each of the remaining $19$ balls can go to any of Boxes $2$–$5$: $4^{19}$ ways. Total $=20\cdot4^{19}$.

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