A printer has 12 colors of ink, but Katie can only pick 4 to use on a pamphlet she is printing. How many different ways can Katie select her 4 colors

495 ways

Step-by-step explanation:

Step one:

we will use the combination formula to solve for the number of ways

given

n= 12

r=4

the formula for the combination is

C(n,r)=(nr)=n!/(r!(n−r)!)=]

Step two:

substituting we have

C(12,4)=(nr)=12!/(4!(12−4)!)=

C(12,4)=(nr)=12!/(4!(8)!)=

C(12,4)=(nr)=12*11*10*9*8!/(4!(8)!)=

C(12,4)=(nr)=12*11*10*9/4!

C(12,4)=(nr)=12*11*10*9/4*3*2*1

C(12,4)=(nr)=11880/24

C(12,4)=(nr)=495ways

the number of ways is 495 ways

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680