Permutation and Combinations — Maths STD 11 Science — Question
CBSE BoardEnglish MediumSTD 11 ScienceMathsPermutation and Combinations2 Marks
Question
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
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Answer
We know that, even number means that the last digit should be even, No. of possible digits at one’s place = 3 (2, 4 and 6) $\Rightarrow$ No. of permutations = $_{1}^{3} \mathrm{P}=\frac{3 !}{(3-1) !}$ = 3 One of a digit is taken at one’s place, Number of possible digits available = 5 $\Rightarrow$ No. of permutations = $_{2}^{5} P=\frac{5 !}{(5-2) !}=\frac{5 \times 4 \times 3 !}{3 !}$ = 20 Thus, a total number of permutations = 3 $\times$ 20 = 60
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