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AP ICET 2015 Paper

Question : 150 of 200

Marks: +1, -0

If a 4 digit number is formed at random without repetition using the digits 0, 1,2, 3, 4, then the probability that the number thus formed is even is

$\frac{3}{5}$
$\frac{2}{5}$
$\frac{5}{8}$
$\frac{3}{8}$

Validate

Solution:

Given digits : 0,1,2,3,4

4-digit number :

III

Total no. of 4–digit numbers (Repetition of digits not allowed ) : I can be filled in 4 ways as it can’t have zero, II can be filled in 4 ways by the remaining

4 digits, III in 3 ways and IV in 2 ways

∴ Total no. of outcomes

=4\times4\times3\times2=96

Similarly,

No. of 4-digit numbers ending with 0

=4\times3\times2=24

No. of 4-digit numbers ending with 2

=3\times3\times2=18

No. of 4-digit numbers ending with 4

=3\times3\times2=18

No. of favourable outcomes

=24+18+18=60

Required probability

=\frac{60}{96}=\frac{5}{8}

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