Question

In how many ways can a constant and a vowel be chosen out of the letters of the word $COURAGE$ ??

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Answer 1

hope it helps you out dude

Answer 2

There are 7 letters in the word COURAGE .

Among them ,

Vowels --> 4 (A,E,O,U)

Consonents ---> 3(C,R,G)


So , one vowel can be choosen from 7 letters in C(7,4) Ways

C(7,4)
= 7!/4!×3!
= 7×6×5/3×2×1
=7×6×5/6
=7×5
=35



Again

3 consonants can be choosen from 7 letters in
C(7,3) ways
So,
C(7,3)
=7!/3!×4!
=7×6×5×4!/3!×4!
=7×6×5/3×2×1
=7×5×6/6
=35



So , one vowel and one consonant can together be choosen in C(7,3)+C(7,4)
Ways

So in 35+35 ways
=70 ways