Question

The no of ways of arranging five different rings in five fingers (including thumb) of a hand, if a finger can have any number of rings, is

• A. ${}^9{P}_5$
• B. ${}^9{C}_5$
• C. $5^5$
• D. $5!\times 5$

Answer 1

The correct option is A ${}^9{P}_5$

Number of ways to place $1^{st}$ ring $=5$

Number of ways to place $2^{nd}$ ring $=6$

[Either in $4$ remaining fingers or above or below of $1^{st}$ ring]

Number of ways to place $3^{rd}$ ring $=7$

Number of ways to place $4^{th}$ ring $=8$

Number of ways to place $5^{th}$ ring $=9$

Total number of ways $=5\times 6\times 7\times 8\times 9=\frac{9!}{4!}={}^9{P}_5$