First slide

Permutations

Question

If the number of five digit numbers with distinct digits and 2 at the 10th place is 336 k, then k is equal to:

Moderate

A

4
B

8
C

6
D

7

Solution

$\begin{array}{l} 2 \end{array}$
The first blank can be filled with any one of the digits 1,3,4,5,6,7,8,9 in 8 ways
The second blank can be filled with any one of the digits 0,1,3,…, without taking first digit, in 8 ways
The third blank can be filled with the remaining 7 digits in 7 ways
And the unit place can be filled with the remaining 6 digits in 6 ways
Hence the number of numbers $= 8 \times 8 \times 7 \times 6 = 2688 = 336 \cdot k \Rightarrow k = 8$

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