Question

5. + 0/4 points | Previous Answers StatsByLO1 9.10.010.CH. A set of license plates has four letters followed by 5 digits. (a) In how many ways can a license plate be made with four letters followed by 5 digits? (Letters or digits may be repeated.) 4569760 x (b) In how many ways can a license plate be made with four different letters followed by 5 different digits? Enter an exact number. (c) If a license plate is made with four letters followed by 5 digits, what is the probability that it has no repeated letters or digits? (Enter your probability as a fraction.) 0.2374

Answer 1

(a) We have 26 Alphabets and 10 digits. Since repetition is allowed, therefore total ways = 26⁴ * 10⁵ = 45697600000

(b) Now repetition is not Allowed. All must be distinct.

The 4 alphabets can be arranged in 26 * 25 * 24 * 23 = 358800 ways

The digits can be arranged in 10 * 9 * 8 * 7 * 6 = 30240 ways

Therefore the total number of ways = 358800 * 30240 = 10850112000

(c) The probability = Favorable outcomes / Total Outcomes

= 10850112000 / 45697600000

= 169533 / 714025

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(c) P(Democrat given that he is a male) = P(D / M) = P( D and M) / P(M)

P(M) = (0.6 * 0.35) + (0.35 * 0.30) + (0.45 * 0.35) = 0.21 + 0.105 + 0.1575 = 0.4725

P(D and M) = 0.6 * 0.35 = 0.21

Therefore the required probability = 0.21 / 0.4725 = 4/9 (0.444)

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