2.1. How many 9-digit numbers divisible by 5 can be formed by rearranging the digits of the number 377353752?
Answer: 1120. Solution. Since the number is divisible by 5, the digit in the 9th place can only be five. After this, we need to distribute the remaining 8 digits across the 8 remaining places: 3 sevens, 3 threes, a five, and a two. The total number of permutations will be 8!, but since there are repeating digits, the answer will be: $\frac{8!}{3!3!}=\frac{2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8}{2 \cdot 3 \cdot 2 \cdot 3}=4 \cdot 5 \cdot 7 \cdot 8=1120$.