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How many odd numbers less than 1000 can be formed using the digits 0, 2, 5, 7 repetition of digits are allowed? |
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Answer» Since the required numbers are less than 1000 therefore, they are 1-digit, 2-digit or 3-digit numbers. One-digit numbers. Only two odd one-digit numbers are possible, namely, 5 and 7. Two-digit numbers. For two-digit odd numbers the unit place can be filled up by 5 or 7 i.e., in two ways and ten’s place can be filled up by 2, 5 or 7 (not 0) in 3 ways. ∴ No. of possible 2-digit odd numbers = 2 × 3 = 6. Three-digit numbers. For three-digit odd numbers, the unit place can be filled up by 5 or 7 in 2 ways. The ten’s place can be filled up by any one of the digits 0, 2, 5, 7 in 4 ways. The hundred’s place can be filled up by 2, 5 or 7 (not 0) in 3 ways. ∴ No. of possible 3-digit numbers = 2 × 4 × 3 = 24 Hence total number of odd numbers = 2 + 6 + 24 = 32. |
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