A probability problem by Vinay Agarwal

Probability Level 3

HOW MANY 3-DIGIT NUMBERS HAVING DISTINCT DIGITS ARE THERE WHICH CAN BE FORMED USING DIGITS 1,2,3,4,5,9 SUCH THAT SUM IS AT LEAST 12 ?


The answer is 66.

Vinay Agarwal by Vinay Agarwal , 24, India

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2 solutions

Vikas Kumar Singh
Jun 12, 2014

3!*6C3 = 120 total three digits numbers total numbers whose sum is less than 12 = 54 so total numbers whose sum at least 12 = 120-54 = 66

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Jayanta Mandi
Feb 23, 2014

5C2* 3! + 3!=66

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how and why?? please elaborate..

Nishant Shandilya - 7 years, 3 months ago

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first cosidering 9 as one digit and selecting 2 nos from 5 . ie nC2 now changing th eplaces(951,915.....etc) so multiply nc2 by 3! now c considering nos not containig 9 and thy are 345 354 435 .... etc

therefoe the tottal nc2 * 3! +3!

kaivalya swami - 7 years, 1 month ago

first cosidering 9 as one digit and selecting 2 nos from 5 . ie nC2 now changing th eplaces(951,915.....etc) so multiply nc2 by 3! now c considering nos not containig 9 and thy are 345 354 435 .... etc

therefoe the tottal nc2 * 3! +3!

kaivalya swami - 7 years, 1 month ago

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