Question: If 7 children are playing hide and seek, then the total number of ways in which exactly 4 get into t...

Question

If 7 children are playing hide and seek, then the total number of ways in which exactly 4 get into their respective houses is

Answer 1

Solution

The number of ways to choose 4 children out of 7 is $\binom{7}{4} = 35$ . The number of ways to derange the remaining 3 children is $D_3 = 2$ . The total number of ways is $\binom{7}{4} \times D_3 = 35 \times 2 = 70$ .