A) 1560
B) 840
C) 1080
D) 480
Correct Answer: A
Solution :
There can be two types of numbers: (i) Any one of the digits 1, 2, 3, 4 repeats thrice and the remaining digits only once \[i.e.\] of the type 1, 2, 3, 4, 4, 4 etc. (ii) Any two of the digits 1, 2, 3, 4 repeat twice and the remaining two only once \[i.e.\] of the type 1, 2, 3, 3, 4, 4 etc. Now number of numbers of the (i) type \[=\frac{6\ !}{3\ !}{{\times }^{4}}{{C}_{1}}=480\] Number of numbers of the (ii) type \[=\frac{6\ !}{2\ !\ 2\ !}{{\times }^{4}}{{C}_{2}}=1080\] Therefore the required number of numbers \[=480+1080=1560\].
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