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Bunuel
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There are four mango saplings and eight apple saplings. 11 Dec 2024, 01:30
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55% (hard)

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66% (01:46) correct 34% (02:09) wrong based on 256 sessions

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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?

A. 8! * 9P2
B. 8! * 9P4
C. 9! * 9P4
D. 8! * 9P6
E. 9! * 9P6
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B
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There are four mango saplings and eight apple saplings. 11 Dec 2024, 08:01
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\(\_M\_M\_M\_M\_M\_M\_M\_M\_\)


Ways to arrange apple sapling \(= 8!\)

Ways to arrange mango sapling \(= ^9P_4\)

Therefore, combining together \(= 8!\times ^9P_4\)

ANS B
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There are four mango saplings and eight apple saplings. 11 Dec 2024, 08:24
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Apple saplings can be arranged in 8! Ways
There are 9 places to arrange Mango saplings
There are 4 mango saplings so, 9P4 ways
Total arrangements= 8!*9P4
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There are four mango saplings and eight apple saplings. 12 Dec 2024, 22:17
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Can someone explain how 9P4 is derived? Is it because it has to be separated by any of 8 Apple saplings?
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There are four mango saplings and eight apple saplings. 12 Dec 2024, 22:33
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NooNYuki
Can someone explain how 9P4 is derived? Is it because it has to be separated by any of 8 Apple saplings?
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Yes it is.
Here is the illustration.
1A2A3A4A5A6A7A8A9
Because there are 8 apple saplings, there are 9 possible position for mango saplings.
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There are four mango saplings and eight apple saplings. 24 Jan 2025, 07:10
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jozie
NooNYuki
Can someone explain how 9P4 is derived? Is it because it has to be separated by any of 8 Apple saplings?
Yes it is.
Here is the illustration.
1A2A3A4A5A6A7A8A9
Because there are 8 apple saplings, there are 9 possible position for mango saplings.
Show more

Why can't there be 2 apple saplings between 2 mango saplings? What am I missing?. I mean if you place 2 apple saplings adjacent to each other then you have only 8 gaps.Bunuel
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There are four mango saplings and eight apple saplings. 24 Jan 2025, 07:50
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Rohit_842
jozie
NooNYuki
Can someone explain how 9P4 is derived? Is it because it has to be separated by any of 8 Apple saplings?
Yes it is.
Here is the illustration.
1A2A3A4A5A6A7A8A9
Because there are 8 apple saplings, there are 9 possible position for mango saplings.

Why can't there be 2 apple saplings between 2 mango saplings? What am I missing?. I mean if you place 2 apple saplings adjacent to each other then you have only 8 gaps.Bunuel
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The mangos are placed where the numbers are (1, 2, 3, ..., 9). Since no number is adjacent to another, it ensures that no two mangos are planted next to each other.
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There are four mango saplings and eight apple saplings. 10 Oct 2025, 05:18
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the combination will matter in terms of saplings? I considered that only the placement of mango sapling will create new case and hence the total required case will be 9c4

Bunuel


The mangos are placed where the numbers are (1, 2, 3, ..., 9). Since no number is adjacent to another, it ensures that no two mangos are planted next to each other.
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There are four mango saplings and eight apple saplings. 10 Oct 2025, 07:52
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Akarsh97
the combination will matter in terms of saplings? I considered that only the placement of mango sapling will create new case and hence the total required case will be 9c4


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The question assumes that the combinations of saplings matter, not just the placement of the mango ones.

There are 8 apple saplings. Place them first:

_ A _ A _ A _ A _ A _ A _ A _ A _

This creates 9 gaps (underscores). To ensure that no two mango saplings are together, we must choose 4 of these 9 gaps for the mango saplings.

Number of ways = 9C4.

Next, arrange the 8 apple saplings among themselves (8!) and the 4 mango saplings among themselves (4!).

Total arrangements = 9C4 * 8! * 4! = 9P4 * 8!.
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