Without repetition of the numbers, four digit numbers are formed with

1.	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 isA. \(\frac{1}{5}\) B. \(\frac{4}{5}\) C. \(\frac{1}{30}\) D. \(\frac{5}{9}\)
Answer» 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

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 isA. \(\frac{1}{5}\) B. \(\frac{4}{5}\) C. \(\frac{1}{30}\) D. \(\frac{5}{9}\)

Answer»

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

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