priarav wrote:
PLUTO wrote:
Schezwan restaurant offers 5 chicken, prawn, beef, vegetable & tofu entrees served with either garlic or chili sauce. In how many ways can 3 entrees be served if no entry is served more than once?
Answer Options: -
A. 10
B. 60
C. 80
D. 100
E. 120
I appreciate your solution and it is well explained.
Can you please help me understand what I am doing wrong in the following approach,
Stage 1: No of ways to make 1st entree (select 1 base from 5 and select 1 sauce from 2) = 5C1 x 2C1 = 10
Stage 2: No of ways to make 2nd entree (select 1 base from 4 remaining and select 1 sauce from 2) = 4C1 x 2C1 = 8
Stage 3: No of ways to make 3rd entree (select 1 base from 3 remaining and select 1 sauce from 2) = 3C1 x 2C1 = 6
Total number of ways = 10 x 8 x 6 = 480
The problem with your solution is that you have counted each unique meal 6 times.
In your solution, we COULD choose:
- chicken with garlic sauce in stage 1, prawn with chili sauce in stage 2, and beef with garlic sauce in stage 3
or
- chicken with garlic sauce in stage 1, beef with garlic sauce in stage 2, and prawn with chili sauce in stage 3
or
- prawn with chili sauce in stage 1, chicken with garlic sauce in stage 2, and beef with garlic sauce in stage 3
or
- prawn with chili sauce in stage 1, beef with garlic sauce in stage 2, and chicken with garlic sauce in stage 3
or
- beef with garlic sauce in stage 1, prawn with chili sauce in stage 2, and chicken with garlic sauce in stage 3
or
- beef with garlic sauce in stage 1, chicken with garlic sauce in stage 2, and prawn with chili sauce in stage 3
Notice that all 6 meals are the SAME.
Since you have counted each unique meal 6 times, we must divide your answer by 6 to get 460/6 = 80
Does that help?
Cheers,
Brent
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