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he number of functions f from {1, 2, . . . , 20} onto {1, 2, . . . , 20} such that f(k) is a multiple of 3 whenever k is a multiple of 4 is (a) 5! · 6! · 9! (b) 5^6· 15! (c) 6^5· 14! (d) 15! · 6!

he number of functions f from {1, 2, . . . , 20} onto {1, 2, . . . , 20} such that f(k) is a multiple of 3
whenever k is a multiple of 4 is
(a) 5! · 6! · 9!
(b) 5^6· 15!
(c) 6^5· 14!
(d) 15! · 6!
 

Grade:12th pass

2 Answers

Arun
25750 Points
5 years ago

there are 5 elements which are multiple of 4 .  There are 6 elements which are multiple of 3 .

so the elements which are multiple of 4 are only mapped to one in  the elements which are multiple of 3.

for remaining 15 elements we can map to any one of 20 elements.

   65 * 2015

shiya
14 Points
5 years ago
yea. i got this. is it none of the above ?
ans given is d. 
can you hlep with the explantion why its d, if possible.

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