Out of 15 balls, of which some are white and the rest are black, howmany should be white so that the number of ways in which the balls can bearranged in a row may be the greatest possible? It is assumed that the ballsof same color are alike?

Out of 15 balls, of which some are white and the rest are black, howma

1.	Out of 15 balls, of which some are white and the rest are black, howmany should be white so that the number of ways in which the balls can bearranged in a row may be the greatest possible? It is assumed that the ballsof same color are alike?
Answer» Correct Answer - 7 or 8 Let there be r white and (15-r) black balls. Then, total number of permutations of these balls is `15!//r!(15-r)!= .^(15)C_(r )` since r white balls are alike and (15-r) black balls are alike. Therefore, the number of arrangement is `.(15)C_(r )` which is maximum, when `r=(15-1)//2 " or " (15+1)//2`, i.e., r=7 or 8.

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Out of 15 balls, of which some are white and the rest are black, howmany should be white so that the number of ways in which the balls can bearranged in a row may be the greatest possible? It is assumed that the ballsof same color are alike?

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