How many numbers are there in all from 6000 to 6999 (Both 6000 and 6999 included) having all digits same?
How many numbers are there in all from 6000 to 6999 (Both 6000 and 6999 included) having all digits same?
(a) 216 (b) 356 (c) 496 (d) 504
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(c) Total numbers between 6000 to 6999 = 1000. Now, when all the digits are different, then thousands place is always to be filled by 6, next place by any of the remaining 9 digits and the remaining two places by any of the 8 and 7 digits respectively. So, total no. of numbers, when all digits are different = 9 x 8 x 7 = 504. Hence, total no. of numbers, where all digits are same total numbers — numbers where digits are different
= 1000 – 504 = 496
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