Question

The number of five-letter words formed with the letters of the word CALCULUS is_____.

Answer 1

Answer: 1110

$21221$
$CALUS$

Type of word	Number of permutations
2 identical +2 identical +1 different	${}^3{C}_2\cdot {}^3{C}_1\cdot \frac{5!}{2!2!1!}=270$
2 identical +3 different	${}^3{C}_1\cdot {}^4{C}_3\cdot \frac{5!}{2!}=720$
All 5 different	120

$\therefore$ Total number of word $=1110$