2. In 1980 California started using license plates of the form 1ABC123; that is,

Question

2. In 1980 California started using license plates of the form 1ABC123; that is, a single digit followed by three letters then another three letters digits. If we assume that the first digit is non-zero, how many such plates can be issued? 3. We're trying to make a committee to talk about Math 8. We'd like the six-person committee to consist of both faculty and students, but at most two faculty members. If there are 5 faculty members and 20 students willing to be on the committee, how many possible committees can be formed?

Explanation / Answer

2. Total number of plates that can be issued

Total number of digits that can be placed as the first digit = (1-9) = 9

Total number of letter that can be placed as second letter= (A-Z) =26

Same for third letter and fourth letter

Total number of digits that can be placed as the fifth digit = (0-9) =10

same for sixth and seventh

So total ways = 9*26*26*26*10*10*10 = 158184000 ways

Ans 3.

At most 2 faculty members mean 0,1,2 faculty members

Total ways to choose = C(5,0)*C(20,6) + C(5,1)*C(20,5)+C(5,2)*C(20,4)

=8760+5*15504 + 10*4845 = 134730 ways

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