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A real estate broker has 11 unsold houses in Gulmarg colony, Broker planned to sold 4 houses to a perspective buyer. In how many ways can Broker plans to sell houses such that no two of them are next to each other?

A real estate broker has 11 unsold houses in Gulmarg colony, Broker planned to sold 4 houses to a perspective buyer. In how many ways can Broker plans to sell houses such that no two of them are next to each other? Correct Answer 70

GIVEN:

Total Houses = 11

Sold houses = 4

CALCULATIONS:

Initially, let's remove the 4 houses which are going to be sold.

Then we are left with 11 − 4 = 7 houses as numbered below.

_ 1 _ 2 _ 3 _ 4 _ 5 _ 6 _ 7_

Now there are 8 positions as marked as “_ " to place the 4 houses (which the broker sells) among 7 houses such that no two such houses are next to each other.

Number of ways to place 4 houses so that no two are next to each other = 8C4 ways.

⇒ Required number of ways = 8C4 = (8 × 7 × 6 × 5) / (4 × 3 × 2 × 1) = 70

∴ Required number of ways is 70.

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