Answer: 210
Step-by-step explanation:
We know that the number of combinations of n things taken r at a time is given by :-
![C(n,r)=\dfrac{n!}{r!(n-r)!}](https://tex.z-dn.net/?f=C%28n%2Cr%29%3D%5Cdfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D)
So, number of ways to select 3 plants out of 7 = ![C(7,3)=\dfrac{7!}{3!4!}=\dfrac{7\times6\times5\times4!}{6\times 4!}=7\times5=35](https://tex.z-dn.net/?f=C%287%2C3%29%3D%5Cdfrac%7B7%21%7D%7B3%214%21%7D%3D%5Cdfrac%7B7%5Ctimes6%5Ctimes5%5Ctimes4%21%7D%7B6%5Ctimes%204%21%7D%3D7%5Ctimes5%3D35)
Also number of ways to arrange them in 3 positions = 3! = 6
Now , total number of arrangements with 1 plant in each spot = (number of ways to select 3 plants out of 7) x (number of ways to arrange them in 3 positions)
= 35 x 6
=210
Hence, required number of ways = 210