How many sequences of 4 different letters can you make from the letters in the English alphabet:
a) If and letters may be used?
b) If no vowels may be used?
c) If a vowel must come first?
a) If and letters may be used?
b) If no vowels may be used?
c) If a vowel must come first?
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a) If any letters may be used (all different), there are
26 C 4 = 26! / (4! * 22!) = 14950
different words possible.
b) If no vowels, there are only 21 letters to choose from. This gives
21 C 4 = 21! / (4! * 17!) = 5985
words.
c) If a vowel must come first, you have a choice from 5 letters (a,e,i,o,u) for the first letter. The remaining 3 letters are chosen from 25 (all different letters).
This gives
5* ( 25 C 3 ) = 5 * 25! / (3! * 22 ! ) = 11500
words.
26 C 4 = 26! / (4! * 22!) = 14950
different words possible.
b) If no vowels, there are only 21 letters to choose from. This gives
21 C 4 = 21! / (4! * 17!) = 5985
words.
c) If a vowel must come first, you have a choice from 5 letters (a,e,i,o,u) for the first letter. The remaining 3 letters are chosen from 25 (all different letters).
This gives
5* ( 25 C 3 ) = 5 * 25! / (3! * 22 ! ) = 11500
words.