(x^m) times (x^n)=x^(m+n)
(1/8)^5 times (1/8)^3=(1/8)^(5+3)=(1/8)^8=1/(8^8)
The result of rolling a number cube 7 times is a 7-digit number composed of digits 1,2,3,4,5 and 6 so that digits can repeat. The total number of possibilities is 6^7.
The number of possibilities where 4 appears exactly two times is 5^5*(7!-6!/2).
5^5 is the number of 5-digits numbers composed of digits 1,2,3,5 and 6 so that digits can repeat.
7! is the number of permutations of digits 1,2,3,4,4,5 and 6.
6! is the number of permutations of digits 1,2,3,{4,4},5 and 6.
We don't want to subtract all numbers where digits 4 appear side by side. That's why we must divide 6! by 2.
Finally, the probability is P=5^5(7!-6!/2)/7^7
350 / 7 = 50
50 * 2 = 100
100 new members
100 / 10 = 10
10 * 3 = 30
30 are new female members
If I remember right the answer is c
100
75 times 1.333333333333333 equals 100
