1. Tardigrade
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  4. Let m denote the number of four digit numbers such that the left most digit is odd, the second digit from left is even and all four digits are different and n denotes the number of four digit numbers such that the left most digit is even, an odd second digit from left and all four different digits. If m = n k then the value of k equals

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Q. Let $m$ denote the number of four digit numbers such that the left most digit is odd, the second digit from left is even and all four digits are different and $n$ denotes the number of four digit numbers such that the left most digit is even, an odd second digit from left and all four different digits. If $m = n k$ then the value of $k$ equals

Permutations and Combinations

Solution:

$m = 5 · 5 · 8 · 7$
$= 1400$
$n = 4 · 5 · 8 · 7 = 160 · 7 = 1120$
$k =\frac{1400}{1120}=\frac{5}{4}$

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