OlympiadMediumCombinatorics5–6

A locker code is made of two different letters chosen from $A$ , $B$ , $C$ , $D$ in order, followed by one digit from $0$ to $9$ . How many codes are possible?

Um código de cacifo é formado por duas letras diferentes escolhidas de $A$ , $B$ , $C$ , $D$ , por ordem, seguidas de um algarismo de $0$ a $9$ . Quantos códigos são possíveis?

Answer options

Solution

Step 1 of 3

1.First letter: $4$ choices. Second letter: $3$ choices, since it must differ.

A locker code is made of two different letters chosen from AAA, BBB, CCC, DDD in order, followed by one digit from 000 to 999. How many codes are possible?

Answer options

A locker code is made of two different letters chosen from $A$ , $B$ , $C$ , $D$ in order, followed by one digit from $0$ to $9$ . How many codes are possible?