Question

Find the number of words each consisting of $3$ vowels and $3$ consonants that can be formed from the letters of the word $\text{Circumference}$.

• A. $22100$
• B. $40020$
• C. $32400$
• D. $64000$

Answer 1

Answer: (A)

$22100$

There are $3C^{\prime }s$

Number of ways to arrange the consonant

Case : involving $3^{\prime }{C}^{\prime }s,2^{\prime }Cs,1C,1C$ and $2R^{\prime }s$

$1+12+36+3+9+24=85$

Therefore consonants can be arranged in $85$ ways

Arrangements of vowels $=13$

Number of ways of arranging $3$ vowels and $3$ consonants

${=}^6{C}_3=20$

$\Rightarrow$ Total number

$=85\times 13\times 20=22100$