Given letters ABCDEFGH: a. How many strings of length 5 can be formed using the

Question

Given letters ABCDEFGH: a. How many strings of length 5 can be formed using the letters ABCDEFGH is repetitions are not allowed? b. How many strings of part (a) begin with the letter H? c. How many strings of part (a) do not begin with the letter H? d. How many strings of part (a) end with 'FGH' where FGH can be in any order. How many different car license plates can be constructed if license contains 2 letters followed by 4 digits: a. If repetitions are not allowed b. If repetitions are allowed c. If letters cannot repeat but numbers can

Explanation / Answer

Q 19)

Given letters = A B C D E F G H total letters = 8

a)

strings of length 5 without repetation = 8 * 7 * 6 * 5 * 4 = 6720 (as spaces fills up the number of letters available decreases)

b) letters beggining with letter H = 7 * 6 * 5 * 4 = 840 (first space is freezed with the letter H and hence only four spaces left in the string)

c) strings do not start with letter H = 6720 - 840 = 5880

d) string ending with "HGF" = 5 * 4(combination of the first two letters from the remaining letters) * 6 (the internal combination of the letters HGF ) = 120

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