KVPY SA Exam 2016 Question Paper

Question : 65 of 80

Marks: +1, -0

If a 3-digit number is randomly chosen, what is the probability that either the number itself or some permutation of the number (which is a 3-digit number) is divisible by 4 and 5?

$1/45$
$29/180$
$11/60$
$1/4$

Validate

Solution:

We need 3-digit number which is divisible by 4 & 5 both.
i.e. their last two digits are 00, 20, 40, 60 & 80
Now, ending with 00 are '9'.
{100, 200, ……, 900}.
If digit repeat other than '0' then they are {220, 440, 660, 880}
but 220 numbers can be permuted according to the condition as {220, 202}
So, there are '8' other favorable cases.
If the number have no digit repeated like 320.
320 can be permuted in 4 ways.
{302, 230, 320, 203}
So, such numbers are 8 × 4 × 4 = 128
Total favorable = 9 + 8 + 128 = 145
So, required prob.

=145/900=29/180

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