Question

The number of four-letter words formed using the letters of the word $INEFFECTIVE$ are

• A. $1200$
• B. $1340$
• C. $1422$
• D. $1556$

Answer 1

The correct option is C $1422$

Number of repeated words :
$1times=N,C,T,V$
$2times=I,F$
$3times=E$

$=$ {all 4 letters different} + {2 same ,1 different,1 different letters} + {2 same ,2 same letters} + {3 same,1 different letters}

${=}^7{\text{P}}_4{+}^3{\text{C}}_1{\times }^6{\text{C}}_2\times \frac{4!}{2!}{+}^3{\text{P}}_2\times \frac{4!}{2!2!}{+}^1{\text{C}}_1{\times }^6{\text{C}}_1\times \frac{4!}{3!}$

$=840+3\times 15\times 12+3\times 6+1\times 6\times 4$

$=840+540+18+24$

$=1422$ ways

Hence, option ${}^{\prime }{C}^{\prime }$ is correct.