Question

Find number of ways of selection of atleast one vowel and atleast one consonant from the word TRIPLE.

Answer 1

${}^{\prime }TRIPL{E}^{\prime }$

Consonants $=T,R,P,L$

Vowels $=I,E$

Number of consonants$=4$

Number of vowels$=2$

Ways of Selecting at least one consonant $={}^4{c}_1{+}^4{c}_2{+}^4{c}_3{+}^4{c}_4$

$=2^4-1$ (Using binomial theorem)

Ways of selecting at least one vowel $={}^2{c}_1{+}^2{c}_2$

$=2^2-1$ (Using binomial theorem)

Since both selections are made simultaneously,

Total number of ways of selecting at least one vowel and at least one consonant $=(2^4-1)(2^2-1)$

$=(16-1)(4-1)$

$=\left(15\right)\times \left(3\right)$

$=45.$