Answer to Question #186268 in Statistics and Probability for Gazal Gulati

Question

Consider the simple problem of placing four coloured balls: red, blue, green and white in 15

boxes. What are the numbers of distinct ways in which the balls can be placed in these

boxes, if each box can hold only one ball? Also write the generalized formula of this

numerical result.

Answer 1

The black ball box can be selected in 15 ways, the red ball box can be selected in 14 ways, the green ball box can be selected in 13 ways, the white ball box can be selected in 12 ways. Then the total number of ways is 15*14*13*12=32760.

In general, if we have k different balls, which must be placed in n boxes so that each box contains only one ball, then the number of ways is $\frac{{n!}}{{(n - k)!}}$

Answer: 32760 ways