Question: A bar is creating a new signature drink. There are five possible alcoholic ingredients in the drink: rum, vodka, gin, peach schnapps, or whiskey. There are five possible non-alcoholic ingredients: cranberry juice, orange juice, pineapple juice, lime juice, or lemon juice. If the bar uses two alcoholic ingredients and two non-alcoholic ingredients, how many different drinks are possible?

1. 25
2. 50
3. 75
4. 100
5. 3600

Answer: D

Solution and Explanation:

Approach Solution 1:

Choose two alcoholic ingredients for the drink in the first stage.
We can employ combinations because it doesn't matter what order we choose the ingredients in.
We have 5 ingredients, and we can choose 2 of them in 5C2 ways (10 ways)
Therefore, there are 10 ways we can finish stage 1.
We have a video on mentally computing combos (like 5C2) if anyone is interested (see below)

Choose two non-alcoholic ingredients for the cocktail in stage two.
Again, we'll employ combinations.
We have 5 ingredients, and we can choose 2 of them in 5C2 ways (10 ways)
So, there are ten ways we can finish stage 2.
According to the Fundamental Counting Principle (FCP), there are (10)(10) ways to accomplish the two phases (and hence produce a drink) (100 ways)

Approach Solution 2:

A bar is making a brand-new signature beverage. The beverage could contain any one of the following alcoholic substances: rum, vodka, gin, peach schnapps, or whisky. Cranberry juice, orange juice, pineapple juice, lime juice, and lemon juice are the five non-alcoholic options. How many different beverages are available if the bar utilises two alcoholic components and two non-alcoholic ingredients?
The combination of two alcoholic and two non-alcoholic ingredient choices is requested in the question. There is a "and" in the middle.
the word and is plural.
Calculate the first two alcoholic ingredients that you choose.
It comes from -> 5!/2!*3!.
Calculate the choice of two alcoholic ingredients in a similar manner. It comes from -> 5!/2!*3!

The final answer is given by = selection of 2 alcoholic ingredient*
selection of 2 non-alcoholic ingredients, or (5!/2!*3!)*(5!/2!*3!). We must now multiply both to obtain the result.
= 100

D is the correct answer.

Approach Solution 3:

1. There are two spaces for alcoholics and two spaces for non-drinkers.

2. There are two slots for alcoholism: (5X4)(2X1)(5X4)(2X1) = 10
   We use 2 X 1 as the denominator in order to prevent 2 duplicate countings (Rum and Vodka combination is the same with Vodka and Rum combination)
3. We can count for non-alcoholics in the same manner as non-alcoholics. 10 possibilities in all.
4. If (2) and (3) are combined, we get 10 X 10 = 100.
   D is the correct choice.

“A bar is creating a new signature drink. There are five possible alcohol" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, Candidates must have basic qualitative abilities. Quant evaluates a candidate's aptitude for both mathematics and logic. The problem-solving section of the GMAT Quantitative test consists of a question and a list of potential answers. The candidate must choose the right answer by applying maths to the question. The problem-solving section of the GMAT Quant topic is made up of very complicated maths problems that must be solved by using the right maths facts.

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