Level:
Project ID:
1003024601
Accepted:
1
Clonable:
0
Easy:
0
Assume the password for the safe deposit box consists of four different letters from the set \( \{A,B,C,D,E,F,G,H\} \) and four different numbers from the set \( \{1,2,3,4,5,6,7\} \). How many different passwords are there?
\( \binom84 \cdot \binom74 \cdot 8! = 98\,784\,000 \)
\( \frac{8!}{4!}\cdot\frac{7!}{3!}\cdot8!=56\,899\,584\,000 \)
\( \left(\frac{8!}{4!}+\frac{7!}{3!}\right)\cdot8! = 101\,606\,400 \)
\( \left(\binom84+\binom74\right)\cdot8!=4\,233\,600 \)