Question

in a window display at a flower shop, there are 3 spots for 1 plant each. to fill these 3 spots, adam has 7 plants to select from, each of a different type. Selecting from the 7 plants, adam can make how many display arrangements with 1 plant in each spot? (Note: the positions of the unselected plants do not matter.)

Answer 1

Answer: 210

Step-by-step explanation:

We know that the number of combinations of n things taken r at a time is given by :-

$C(n,r)=\dfrac{n!}{r!(n-r)!}$

So, number of ways to select 3 plants out of 7 = $C(7,3)=\dfrac{7!}{3!4!}=\dfrac{7\times6\times5\times4!}{6\times 4!}=7\times5=35$

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