Question

How many different gardens can a farmer plant if he wants one row each of six vegetables?

720
120
36

Answer 1

`6!= \\ 6*5*4*3*2*1= \\ 30*4*3*2*1= \\ 120*3*2*1= \\ 360*2*1= \\ 720*1= \\ 720`

Answer 2

The number of different gardens a farmer can plant is:

720

Explanation:

We are asked to find the different number of arrangements that can be done such that he gets one row each of six vegetables.

i.e. we can arrange 6 numbers in different ways.

This means that we have to use the method of permutation which is used to arrange a specific number of items.

We know that the arrangement of 6 elements is given as:

`6!`

The value of this expression is given as:

`6!=6* 5* 4* 3* 2* 1\\\\6!=720`

Hence, the different gardens that a farmer can plant if he wants one row each of six vegetables is:

720