Question

Consider the set of letters, {L, G, B, T, Q, I, A}: a) How many ways are there to form a string containing exactly one copy of each letter? b) Suppose all license plates in a certain state consist of three distinct consonants followed by two distinct vowels. How many such license plates can be formed from the given set? c) Suppose three letters are chosen from this set at random (repeats allowed); what are the odds that at least one of them is a vowel (rounded to four digits)? Solution:

          Consider the set of letters, {L, G, B, T, Q, I, A}:
a) How many ways are there to form a string containing exactly one copy of each letter?
b) Suppose all license plates in a certain state consist of three distinct consonants followed
by two distinct vowels. How many such license plates can be formed from the given set?
c) Suppose three letters are chosen from this set at random (repeats allowed); what are the
odds that at least one of them is a vowel (rounded to four digits)?

Solution:

Consider the set of letters, L, G, B, T, Q, I, A:
a) How many ways are there to form a string containing exactly one copy of each letter?
b) Suppose all license plates in a certain state consist of three distinct consonants followed
by two distinct vowels. How many such license plates can be formed from the given set?
c) Suppose three letters are chosen from this set at random (repeats allowed); what are the
odds that at least one of them is a vowel (rounded to four digits)?

Solution:

Added by David H.

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