Question

4.
In a certain state, license plates have 2 letters followed by 5 digits. How many different license plates
are possible if
a) digits and letters can be repeated?
b)
digits and letters cannot be repeated?

Answer 1

Answer: A) 26_ 26 10_10_10_10_10 = 67,600,000

B) 26_25 10_9_8_7_6 = 19,656,000

Step-by-step explanation: A) There's exactly 26 letters in the Alphabet and it wants us to repeat it, so write 26_26. Since it's also asking for a 5 digits, write 10 five times because there's only 10 digits; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Multiply the Numbers all-together which is equals 67,600,000.

B). Again, since the License plate has 2 letters, write the Number twice. However it cannot be repeated, so write 26_25. As for the 5 digits write the Number 5 times, but it also can't be repeated, so write 10_9_8_7_6 (Use commas if you want). Then Multiply the Numbers all-together which equals 19,656,000.