15,571 views
6 votes
6 votes
Hi Answer to each option is given as:

a) 122,523,030
b) 72,930,375
c) 223,149,655
d) 100,626,625
And I used the following approach to each option but answers don't match.
a) C(5,1)*C(21,5)*6!
b) C(5,2)*C(21,4)*6!
c) P(26,6)-P(21,6)
d) [C(5,2)*C(21,4)+C(5,3)*C(21,3)+C(5,4)*C(21,2)+C(5,5)*C(21,1)]*6!
Please check.

1 Answer

Best answer
15 votes
15 votes

(a) Six letters with one vowel. We can place the vowel in any of the 6 positions in 5 * 6 ways and the remaining 5 positions can be filled in in 215 ways by the consonants as they can be repeated also. So, total number of words possible

= 215 * 5 * 6 = 122,523,030

(b) Two vowels will give (vowels can also be repeated)

214 * 5 * 5 * 6C2  = 72,930,375

(c) 266 - 216 = 223,149,655

(d) (c) - (a) = 100,626,625

@Sahil-gupta All your answers are correct if letters were not allowed to be repeated. 

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