CAT Quantitative Ability Questions | CAT Permutation, Combination and Probability questions
CAT/2004
Question . 23
Suppose n is an integer such that the sum of the digits of n is 2, and 1010 < n < 1011. The number of different values for n is
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Explanatory Answer
Method of solving this CAT Quantitative Ability Question from Permutation, Combination and Probability question
(a) As 1010 < n < 1011, it means that n has 11 digits. Furthersum of digits of n = 2, it means that either there are 2one’s or a ‘two’ in the whole digit, 2 one’s can beobtained by fixing the first digit as 1 and the remaining10 digits can be organised in 10 ways.In case of one ‘2’ there can be only 1 possibility with2 as the 1st digit.Hence, total no. of different values for n = 10 + 1 = 11.