Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPermutations2 Marks
Question
How many 3-digit numbers are there, with distinct digits, with each digit odd?
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Answer
The odd digits are 1, 3, 5, 7, 9 $\therefore$ Total number of odd diqits = 5 Clearly, the hundred's place can be filled with any of the 5 digits 1, 3, 5, 7 or 9 So, there are 5 ways of filling the hundred's place. Now, 4 digits are left. So, ten's place can be filled with any of the remaining 4 digits in 4 ways. Now, the unit's place can be filled with in any of the remaining 3 digits. So, there are 3 ways of filling the unit's place. Hence, the total number of required number = 5 × 4 × 3 = 60
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