Question

A five-digit number is formed using the digits 0, 2, 3, 4, 5 and 7 with no digit occurring more than once. The probability that the number is divisible by 12 is

Answer 1

Answer:

$\frac{3}{8}$

Step-by-step explanation:

divisibility law by 4 is last two digits should be divided by 4 . (number will always be divided by 3 since 0+2+3+4+5+7 = 21 )

Possible cases : 20 , 40 , 32 , 52 , 72 , 04 , 24 ,

total such numbers

= 3×( 0 is in last two digits) + 4× ( it is not )

= 3×(3! - 2!)+ 4× (3!) = 36

(Note : remove the case when 0 comes at first place then it is actually 4 digit number )

Now

Total numbers = 5! - 4! = 96

So required probability = 36/96 = 3/8