Question

Deepak is choosing a password for his phone using letters from the alphabet, A-Z. The password must be four letters long, and he can repeat letters. How many different passwords can he create?

Answer 1

Answer: 26 × 4

Step-by-step explanation: There are 26 letters in the alphabet lettered A through Z.

Deepak is given the choice of picking a four letter password of his liking, using any four letters. Since the letters he uses can be repeated, it is 26 * 4 possibilities, since there are 26 different possibilities of letters from the alphabet he could choose, for 4 times. Also, since letters can be repeated, 26 stays the same. If letters could not be repeated, it would be 26 * 25 * 24 * 23.

Answer 2

B. 26⁴

Explanation:

If the password is 4 letters long and he can repeat letters then:

• 1st letter: any one of the 26 letters from the alphabet
• 2nd letter: any one of the 26 letters from the alphabet
• 3rd letter: any one of the 26 letters from the alphabet
• 4th letter: any one of the 26 letters from the alphabet

Therefore, to find the total number of passwords he can create, simply multiply the number of permutations for each letter of his password:

⇒ 26 × 26 × 26 × 26 = 26⁴