Question: In how many ways the letter of the word "Family" can be when F and Y occur together?

A) 120
B) 24
C) 240
D) 48

Correct Answer: (C)

Solution and Explanation:
Approach Solution 1:

The problem statement asks to find the number of ways the letter of the word "Family" can be if F and Y occur together.

Let’s consider F and Y as one unit that is {FY}.

Now the 5 units {FY}, {A}, {M}, {I}, {L} can be positioned in 5! ways. Moreover, F and Y can be positioned in 2! within their units.
Therefore, the total number of ways the letter of the word "Family" can be 5!*2!=240.

Approach Solution 2:

The problem statement questions how to discover the number of ways the letter of the word "Family" can be if F and Y occur together.

The problem can be split into 3 sections to promote better understanding. The word 'Family' has 6 letters and it is stated to keep F and Y together:

1. Listing different possibilities of positioning F and Y
2. Positioning the remaining 4 letters around F and Y
3. Positioning F and Y between themselves

1. The set F and Y can appear in any of the two positions within the 6 positions i.e. 5 ways

F Y _ _ _ _
_ F Y _ _ _
_ _ F Y _ _
_ _ _ F Y _
_ _ _ _ F Y

2. The remaining 4 letters can be positioned in the blank spaces ("_") shown in point a.

F Y 4 3 2 1 =24
4 F Y 3 2 1 =24
4 3 F Y 2 1 =24
4 3 2 F Y 1 =24
4 3 2 1 F Y =24

100. Finally, F and Y can be positioned in 2 ways i.e F Y and Y F

Therefore, by combining b and c we get,

(24∗5)∗2=240

Approach Solution 3:

The problem statement questions how to find the number of ways the letter of the word "Family" can be if F and Y occur together.

Let's consider (FY) as one entity, then the total quantity is 5

Therefore, (FY) (AMIL) = 1 + 4 = 5

5! = 5 x 4 x 3 x 2 x 1 = 120

Therefore, in the next step, we can consider. FY can be changed internally in 2 ways

120 x 2 = 240 ways.

“In how many ways the letter of the word "Family" can be when''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions enhance the skills of the candidates and make them proficient enough to crack the GMAT exam. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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