Question 849405
<pre>
COURAGE has 3 consonants and 4 vowels</pre>
how many permutations can be obtained by letter COURAGE if:

(a)constants occupy the even places,<pre>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</pre>(b)A and E occupy the ends,<pre>5! ways for A _ _ _ _ _ E and 5! for E _ _ _ _ _ A

Answer:  2×5! = 2×120 = 240 ways</pre>(c)C and E come together?<pre>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</pre>