COURAGE has 3 consonants and 4 vowels
how many permutations can be obtained by letter COURAGE if:
(a)constants occupy the even places,V C V C V C V
Choose the 2nd letter as a consonant 3 ways.
Choose the 4th letter as a consonant 2 ways.
Choose the 2nd letter as a consonant 1 way.
Choose the 1st letter as a vowel 4 ways.
Choose the 3rd letter as a vowel 3 ways.
Choose the 5th letter as a vowel 2 ways.
Choose the 7th letter as a vowel 1 way.
Answer 3×2×1×4×3×2×1 = 3!4! = 6×24 = 146 ways
(b)A and E occupy the ends,5! ways for A _ _ _ _ _ E and 5! for E _ _ _ _ _ A
Answer: 2×5! = 2×120 = 240 ways
(c)C and E come together?That's the number of permutations of the 6 things {CE,O,U,R,A,G)
plus the number of permutations of the 6 things {EC,O,U,R,A,G)
That's 2×6! = 2×720 = 1440 ways.
Edwin
