If each coded item in a catalog begins with 3 distinct letters followed by 4 distinct nonzero digits, ﬁnd the probability of randomly selecting one of these coded items with the ﬁrst letter a vowel and the last digit even.

Question

Jakobe Henry

Mathematics

23 February, 15:00

If each coded item in a catalog begins with 3 distinct letters followed by 4 distinct nonzero digits, ﬁnd the probability of randomly selecting one of these coded items with the ﬁrst letter a vowel and the last digit even.

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Answers (1)

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Jacob Stanley · Answer 1

Answer: 10/117

Step-by-step explanation:

3 distinct letters and 4 distinct nonzero digits

For letters: A → Z = 26 options

For numbers: 1 → 9 = 9 options

As we have 26 options for letters and 9 for numbers and they have to be distinct, for the total of codes we have

Total of codes: 26.25.24.9.8.7.6

For the particular code asked, we have 5 options of vowels and 4 options of even numbers, so

5.25.24.8.7.6.4

probability: 5.25.24.8.7.6.4 = 10

26.25.24.9.8.7.6 117