Sai has five cards.
1,5,4,6,7
how many three digit numbers can she make with these cards which are di isible by 6?

Dear Student,

Please find below the solution to the asked query:

We know any number is divisible by 6 if sum of all digits is divisible by 2 and 3 .

By 1 , 5 , 4 , 6 , 7  , We get numbers  :

154 , 156 , 157 , 145 , 146 , 147 , 164 , 165 , 167 , 174 , 175 , 176 , 415 , 416 , 417 , 451 , 456 , 457 , 461 , 465 , 467 , 471 , 475 , 476 , 514 , 516 , 517 , 541 , 546 , 547 , 561 , 564 , 567 , 571 , 574 , 576 , 614 , 615 , 617 , 641 , 645 , 647 , 651 , 654 , 657 , 671 , 674 , 675 , 714 , 715 , 716 , 741 , 745 , 746 , 751 , 754 , 756 , 761 , 764 , 765

And out these numbers we get numbers that have sum divisible by 2 and 3 and last digit is a even number , As :

156 =  1 + 5 + 6 =  12 and 12 is divisible by 2 and 3

Like  156 we get  174 , 516 , 576 , 714 , 741 , 756 .

So,

Total numbers divisible by 6 ( 156 , 174 , 516 , 576 , 714 , 741 , 756 ) = 7                              ( Ans )


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