JEE PYQ: Permutation And Combination Question 24
Question 24 - 2020 (07 Jan Shift 1)
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is:
(1) $\frac{1}{2}(6!)$
(2) $6!$
(3) $5^6$
(4) $\frac{5}{2}(6!)$
Show Answer
Answer: (4)
Solution
One digit repeats. Choose which digit repeats: ${}^5C_1 = 5$. Arrange 6 digits (with one repeated twice): $\frac{6!}{2!}$. Total $= 5 \times \frac{6!}{2!} = \frac{5}{2}(6!)$.
BETA
