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

Hint: In this question, we have a total of 3 coins. For the 1st case when Taking 3 coins of 1 Rs. And other 2 coins consist of combinations of Rs. 2 and Rs. 5. Similarly Taking 3 coins of 2 Rs. And taking the rest of them 2 coins consist of combinations of Rs. 1 and Rs. 5 as discussed below. And similarly done for case 3, when Taking 3 coins of 5 Rs.

Complete step-by-step answer:
Now,
As mentioned in the question
We need to select the Number of ways of selecting 5 coins from coins three each of Rs. 1, Rs. 2 and Rs. 5.
when 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.

when 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.

when 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.
∴ Total number of ways =3+3+3=9.
Thus, option (A) is the correct answer.

Note- As already mentioned in the question, we need to find the Number of ways of selecting 5 coins from coins three each of Rs. 1, Rs. 2 and Rs. 5. Since coins of the same denomination are alike, we have to take the first 3 coins consisting of only Rs. 1 or Rs. 2 or Rs. 5.