A) 9.7!
B) 8!
C) 5!.4!
D) 8!.4!
Correct Answer: A
Solution :
Number of digits are 9 Select 2 places for the digit 1 and 2 in \[^{9}{{C}_{2}}\] ways from the remaining 7 places select any two places for 3 and 4 in \[^{7}{{C}_{2}}\] ways and from the remaining 5 places select any two for 5 and 6 in \[^{5}{{C}_{2}}\] ways Now, the remaining 3 digits can be filled in 3! ways \[\therefore \]Total ways \[{{=}^{9}}{{C}_{2}}{{.}^{7}}{{C}_{2}}{{.}^{5}}{{C}_{2}}.3!\] \[=\frac{9!}{2!.7!}.\frac{7!}{2!.5!}.\frac{5!}{2!.3!}.3!=9.7!\]
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