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A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4, and 5 without repetitions. The total number of ways this can be done is:

(a) 216

(b) 600

(c) 240

(d) 3125

[Hint: 5-digit numbers can be formed using digits 0, 1, 2, 4, 5 or by using digits 1, 2, 3, 4, 5 since the sum of digits in these cases is divisible by 3.]

0 4 Views | Posted 3 months ago
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  • 1 Answer

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    Answered by

    Payal Gupta | Contributor-Level 10

    3 months ago

    This is an Objective Type Questions as classified in NCERT Exemplar

    W e     k n o w     t h a t     a     n u m b e r     i s     d i v i s i b l e     b y     3     w h e n     t h e     s u m     o f     i t s     d i g i t s     i s     d i v i s i b l e     b y     3 . I f     w e     t a k e     t h e     d i g i t s     0 , 1 , 2 , 4 , 5 ,     t h e n     t h e     s u m     o f     t h e     d i g i t s = 0 + 1 + 2 + 4 + 5 = 1 2     w h i c h     i s d i v i s i b l e     b y     3 . So,  the  5  digit  numbers  using  the  digits  0,1,2,4  and  5                               T T H 4           T H 4           H 3           T 2             O 1                             = 4 × 4 × 3 × 2 × 1 = 9 6 a n d     i f     w e     t a k e     t h e     d i g i t s     1 , 2 , 3 , 4 , 5 ,     t h e n     t h e i r     s u m                               = 1 + 2 + 3 + 4 + 5 = 1 5     w h i c h     i s     d i v i s i b l e     b y     3 . So,  the  5  digit  numbers  can  be  formed  using  the  digits  1,2,3,4,5  is  5!  ways                               = 5 × 4 × 3 × 2 × 1 = 1 2 0 T o t a l     n u m b e r     o f     w a y s = 9 6 + 1 2 0 = 2 1 6 H e n c e ,     t h e     c o r r e c t     o p t i o n     i s     ( a ) .

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