Consider set of all 7- digit numbers formed by digits 0,1,2,3,4,5,6 , each chosen exactly once. If a

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14.Probability

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Consider the set of all $7-$digit numbers formed by the digits $0,1,2,3,4,5,6$, each chosen exactly once. If a number is randomly drawn from this set, the probability that it is divisible by $4$ is

A

$\frac{26}{105}$

B

$\frac{13}{45}$

C

$\frac{2}{7}$

D

$\frac{1}{3}$

(KVPY-2021)

Solution

(b)

$\{0,1,2,3,4,5,6\}$

Total $=7 !-6 !=6.6 !$

fav : last two digit $\{12,16,24,32,36,52,56,64\}$

$8(5 !-4 !)$

last two digit $\{04,20,40,60\}$

$4.5 !$

fav $=8(5 !-4 !)+4.5 !$

fav $=32.4 !+20.4 !=52.4 !$

$P =\frac{\text { fav }}{\text { Total }}=\frac{52.4 !}{180.4 !}=\frac{13}{45}$

Standard 11

Mathematics

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