Jane must select three different items for each dinner she will serve.

Question

Jane must select three different items for each dinner she will serve. The items are to be chosen from among five different vegetarian and four different meat selections. If at least one of the selections must be vegetarian, how many different dinners could Jane create?

A. 30

B. 40

C. 60

D. 70

E. 80

A. 30

B. 40

C. 60

D. 70

E. 80

RB15 · Accepted Answer

For at-least 1 vegetarian selection, we can calculate (total possibilities - only meat selections)

=> 9C3 - 4C3 = 80

Ans : E

EgmatQuantExpert · Answer

Solution

Given:  
• 3 different items need to be chosen for dinner, of which at least one item must be vegetarian selection
• Options available:
 o 5 different vegetarian selections
o 4 different meat selections

To find:  
• How many different dinners Jane could create

Approach and Working:   
• Out of total 9 items, number of ways 3 items can be chosen =  ^9C_3 
• If all the choices made are meat items, number of ways it can be done =  ^4C_3 
• Hence, to ensure at least 1 vegetarian item is selected, number of ways choices can be done =  ^9C_3  –  ^4C_3 = 84 – 4 = 80

^5C_1* ^4C_2 + ^5C_2 * ^4C_1 + ^5C_3 = 5*6 + 10 * 4 + 10 = 30 + 40 + 10 = 80 ]

Hence, the correct answer is option E.

Answer: E

Paras96 · Answer

Jane must select three different items for each dinner she will serve. The items are to be chosen from among five different vegetarian and four different meat selections. If at least one of the selections must be vegetarian, how many different dinners could Jane create?

A. 30

B. 40

C. 60

D. 70

E. 80

As per given scenario, 
Total dinners with at least 1 selection vegetarian = Total dinners with no restrictions - Total dinners with no vegetarian 
=> Total dinners with at least 1 selection vegetarian = 9C3 - 4C3 = 80

Hence E

flippedeclipse · Answer

The phrase "at least" keys us in to use the complement method. The word "chosen" indicates combination.

There are three possible cases that satisfy the requirement of at least one vegetarian dish:
1. 1 veg, 2 meat
2. 2 veg, 1 meat
3. 3 veg

Instead of calculating each of them, we can take the total number without the restrictions and subtract the number of ways 3 meat dishes could be picked, which allows us to find the value of the three cases listed above.

Total # of arrangements:  9C3=\frac{9*8*7}{3*2}=84

Arrangements of just meat:  4C3=\frac{4*3*2}{3*2}=4

At least 1 vegetarian dish:  84-4=80

Thus answer is E.

Jane must select three different items for each dinner she will serve.

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GMAT Problem Solving (PS) Questions

Jane must select three different items for each dinner she will serve.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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