Question: There are four mango saplings and eight apple saplings. In how many ways can they be planned in a row, such that NO two mango saplings are together?
- 8! * 9P2
- 8! * 9P4
- 9! * 9P4
- 8! * 9P6
- 9! *9P6
Correct Answer: B
Solution and Explanation
Approach Solution 1:
It is asked to find how in many ways can planting seeds be planned in a row, such that NO two mango saplings are together
Let us evaluate further-
Eight apple saplings can be arranged in eight different ways.
There will be 9 gaps between the 8 apple saplings.
Four mango saplings will be arranged in 9P49P4 configurations.
Total number of ways: 8! * 9P4
8! * 9P4 ways planting seeds can be planned in a row, such that NO two mango saplings are together
Approach Solution 2:
There is another approach to solving this question which is fairly simple and graphic to present, let us see it further-
it is asked to find how in many ways planting seeds can be planned in a row, such that NO two mango saplings are together when There are four mango saplings and eight apple saplings.
First, plant 8 apple saplings with gaps in 8! different directions.
_1_ 2_ 3_ 4_ 5_ 6_ 7_ 8_
The nine gaps thus formed can be used to arrange four mango saplings in 9P4.
Total number of ways: 8! * 9P4
8! * 9P4 ways planting seeds can be planned in a row, such that NO two mango saplings are together
Approach Solution 3:
Eight apple saplings can be arranged in 8! ways.
There will be a total of 9 gaps between 8 apple saplings.
Four mango saplings will be arranged as 9P49P4 ways.
Total ways: 8! * 9P4
“There are four mango saplings and eight apple saplings. In how”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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