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$If n_{1}, n_{2} are the number of 5 digit numbers in which the digits occur in increasing and$ $decreasing orders respectively and n_{2} - n_{1} = {}^{n}C_{r}, then a possible value of n + r is$

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answer is B.

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Detailed Solution

$\begin{array}{l} n_{1} = 9 c_{5}, = selections of 5 digits from 9 non-zero digits \\ n_{2} =^{10} C_{5} = selections of 5 digits from 0 to 9 \\ n_{2} - n_{1} =^{9} C_{5} {or}^{9} C_{4} \end{array}$

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