JEE PYQ: Permutation And Combination Question 45
Question 45 - 2019 (11 Jan Shift 2)
The number of functions $f$ from ${1, 2, 3, \ldots, 20}$ onto ${1, 2, 3, \ldots, 20}$ such that $f(k)$ is a multiple of 3, whenever $k$ is a multiple of 4 is:
(1) $6^5 \times (15)!$
(2) $5! \times 6!$
(3) $(15)! \times 6!$
(4) $5^6 \times 15$
Show Answer
Answer: (3)
Solution
Multiples of 4 in domain: 4, 8, 12, 16, 20 (5 elements). These must map to multiples of 3: 3, 6, 9, 12, 15, 18 (6 elements). Ways $= {}^6C_5 \times 5! = 6 \times 5! = 6!$. Remaining 15 elements map to remaining 15 elements: $15!$. Total $= 15! \times 6!$.
BETA
