Question

Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is

A.  \(\frac{1}{5}\) 

 B.  \(\frac{4}{5}\) 

 C. \(\frac{1}{30}\) 

D.  \(\frac{5}{9}\)

Answer 1

Total numbers of 4digit that can be formed using 0,2,3,5 without repetition= 3× 3 × 2 × 1 = 18 

For number to be divisible by 5 unit digit must end with 5 or 0. 

∴ total such numbers(4 digit) ending with zero are = 3× 2× 1(0 is fixed at the unit digit) = 6 

∴ total such numbers(4 digit) ending with zero are = 2× 2× 1(5 is fixed at the unit digit) = 4 

Total 4 digit numbers using given digit divisible by 5 are 6 + 4 =10 

∴ P(a number divisible by 5) = \(\frac{10}{18}\) = \(\frac{5}{9}\)

As our answer matches only with option (d) 

∴ Option (d) is the only correct choice