The general manager of a fast-food restaurant chain must choose
six restaurants from among 18 for a
promotional program. In how many
ways can the six restaurants be
chosen? (Hint: First, determine if this
problem requires the permutation or the
combination formula.)

18564

Step-by-step explanation:

In the problem Given, we just need to see t any 6, the order of selection does not matter, hence, this is a combination problem :

Using the combination relation :

nCr = 18C6

Recall ;

nCr = n! / (n-r)!r!

18C6 = 18! / (18-6)!6!

18C6 = 18! / 12!6! = (18*17*16*15*14*13) / (6*5*4*3*2*1)

18C6 = 13366080 / 6!

18C6 = 18564

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet