The number of functions f from {1, 2, 3, ..., 20} onto {1, 2, 3, ..., 20} such that f(k) is a multiple of 3, whenever k is a multiple of 4, is :-

a. |
(15)! × 6! |
b. |
5 |

c. |
5! × 6! |
d. |
6 |

The number of functions f from {1, 2, 3, ..., 20} onto {1, 2, 3, ..., 20} such that f(k) is a multiple of 3, whenever k is a multiple of 4, is :-

a. |
(15)! × 6! |
b. |
5 |

c. |
5! × 6! |
d. |
6 |

1 Answer

127 votes

f(k) = 3m (3,6,9,12,15,18)

for k = 4,8,12,16,20 6.5.4.3.2 ways

For rest numbers 15! ways

Total ways = 6!(15!)

127 votes

127