Question

Number of ways of selecting $5$ coins from coins three each of Rs. $1$, Rs. $2$ and Rs. $5$ if coins of the same denomination are alike, is:

• A. $9$
• B. $12$
• C. $21$
• D. None

Answer 1

The correct option is A $9$

(1) Taking 3 coins of 1 Rs. :-

Case 1 - (a) 2 coins of 2 Rs.

(b) 1 coin of 2 Rs and 1 coin of Rs 5.

(c) 2 coins of 5 Rs.

(2) Taking 3 coins of 2 Rs. :-

Case 2 - (a) 2 coins of 1 Rs.

(b) 1 coin of 1 Rs and 1 coin of Rs 5.

(c) 2 coins of 5 Rs.

(3) Taking 3 coins of 5 Rs. :-

Case 3 - (a) 2 coins of 1 Rs.

(b) 2 coins of 2 Rs.

(c) 1 coin of 1 Rs and 1 coin of 2 Rs.

$\therefore$ Total number of ways $=3+3+3=9$.