Question

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? 

(A) 1/45

(B) 29/180 

(C) 11/60

(D) 1/4 

Answer 1

Correct Option :- (B)29/180

Explanation :-

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