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Permutations and Combination — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsPermutations and Combination4 Marks
Question
How many five-digit numbers formed using the digit 0, 1, 2, 3, 4, 5 are divisible by 5 if digits are not repeated?
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Answer

Here, repetition of digits is not allowed. For a number to be divisible by 5, unit’s place digit should be 0 or 5. Case I: when unit’s place is 0 Unit’s place digit can be selected in 1 way. 10’s place digit can be selected in 5 ways. 100’s place digit can be selected in 4 ways. 1000’s place digit can be selected in 3 ways. 10000’s place digit can be selected in 2 ways. ∴ Total number of numbers = 1 × 5 × 4 × 3 × 2 = 120. Case II: when the unit’s place is 5 Unit’s place digit can be selected in 1 way. 10000’s place should be a non-zero number. ∴ It can be selected in 4 ways. 1000’s place digit can be selected in 4 ways. 100’s place digit can be selected in 3 ways. 10’s place digit can be selected in 2 ways. ∴ Total number of numbers = 1 × 4 × 4 × 3 × 2 = 96 ∴ Total number of required numbers = 120 + 96 = 216

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