Question: 1. (10 points) Combinatorial Analysis You want to generate a four-digit PIN (digits can range from 0 to 9) (a) How many PIN combinations are

1. (10 points) Combinatorial Analysis You want to generate a four-digit

1. (10 points) Combinatorial Analysis You want to generate a four-digit PIN (digits can range from 0 to 9) (a) How many PIN combinations are there? (b) How many PIN combinations are there if no digit may occur more than once? (e.g. "6294" but NOT "6264" ) (c) How many PIN combinations are there if no digit may occur more than once and the digits have to be sorted from lowest to highest? (e.g. "2469" but NOT "6294") (d) How many PIN combinations are there such that the sum of the four digits adds up to nine ? (e.g. "1234", since 1 + 2+ 3 + 4 = but NOT "1111")

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