Mathematics - Permutation & Combination Question with Solution | TestHub

There are 2 vowels and 4 consonants in the letters $a,b,c,d,e,f$. If we select one vowel, then number of arrangements $$={}^2{C}_1\times {}^4{C}_2\times 3!=2\times \frac{4\times 3}{2}\times 3\times 2=72$$ If we select two vowels, then number of arrangements $$={}^2{C}_2\times {}^4{C}_1\times 3!=1\times 4\times 6=24$$ Hence, total number of arrangements $$=72+24=96$$