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Q.
A six digit number is formed with the digits $0, 1, 2, 3, 4, 7$ without repetition. Then the probability that it is divisible by $4$, is
Probability
Solution:
If the $6$ digit number is to be divisible by $4$,
the last two digits have to be one of the following pairs
$04,12,20,24,32,40, 72$.
$\therefore $ The number of favourable ways
$\lfloor4+3\cdot3\cdot2\cdot1+\lfloor4 +3\cdot3\cdot2\cdot1 +3\cdot3\cdot2\cdot1 $
$+\lfloor4 +3\cdot3\cdot2\cdot1 = 144$.
Total number of numbers that can be formed
$= 6! - 5! = 5! (6 - 1) = 600 $
Hence the probability $=\frac{144}{600}$
$ = \frac{6}{25}$.