AMC 12 2004a Problem 4

Bertha has $6$ daughters and no sons. Some of her daughters have $6$ daughters, and the rest have none. Bertha has a total of $30$ daughters and granddaughters, and no great-granddaughters. How many of Bertha's daughters and grand-daughters have no daughters?

$\text{(A) } 22 \text{(B) } 23 \text{(C) } 24 \text{(D) } 25 \text{(E) } 26$