Fundamental Counting Principle

Probability Level pending

How many three digit positive integers are there for which the unit digit is not equal to the hundreds digit.


The answer is 810.

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Zee Ell
Jul 3, 2017

There are 999 - 99 = 900 positive three digit integers.

The number of positive three digit integers, for which the unit digit is equal to the hundreds digit: 9 × 10 = 90, since we can choose the first (and 3rd, as they are equal) digit 9 ways (1 to 9, since we cannot start with a zero) and the 2nd digit 10 ways (0 to 9).

Hence, our answer should be:

900 − 90 = 810 900 - 90 = \boxed {810}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Yes, correct or we can say 9 9 choices for the hundred's digit since 0 0 can't take that place, 10 10 choices for the tens digit and since the ones digit is not equal to the tens digit, also, we have 9 9 choices for the ones digit ⟹ 9 × 10 × 9 = 810 \implies9\times 10\times 9= 810 .

Hana Wehbi - 3 years, 11 months ago

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