Class 11

Math

Algebra

Permutations and Combinations

Five - digit numbers divisible by 3 are formed using 0, 1, 2, 3, 4, 5 without repetition. The total number of such numbers is :

- 312
- 3125
- 120
- 216

Numbers using $1,2,3,4,5(1+2+3+4+5=15)$

$⇒$ The number of choices we have $=5!=120$

Numbers using $0,1,2,4,5(0+1+2+4+5=12)$

$⇒$ The number of choices we have $=5!−4!$

$=120−24$

$=96$

There are $4!$ numbers beginning with $0$

$∴$ Total number of numbers $=120+96=216$