How many strings of English letters contain exactly 3 z’s and 3 w’s with length 8

combinatorics

since it is AND and not OR I figure after you find the number of strings that exactly contain 3 of each kind you simply square this number. I am just not sure how to calculate it.

Best Answer

The three $z$s can be placed in ${8 \choose 3}$ ways. The three $w$s can then be placed in ${5 \choose 3}$ ways. The remaining two slots can have $24$ letters in the first place and $24$ letters in the second place.

Multiply these: $322560$.