Question

Ms. Swan is redecorating her office. She has a choice of 7 color of paint, 4 kinds of curtain, 3 colors of carpet, and 2 style of furniture. How many different ways are there to redecorate if she chooses 2 different colors of paint, 1 kind of curtain, 1 color of carpet, and 1 style of furniture.

Answer 1

She can choose 2 different colors from 7 colors in 7(C)2 ways..
She can choose 1 kind of Curtain from 4 kind of Curtain in : 4(C)1
She can choose 1 color of Carpet from 3 colors of Carpet in: 3(C)1
She can choose 1 style of Furniture from 2 Style of Furniture in : 2(C)1

S0, the required answer will be: MULTIPLY ALL THE TERMS..

Answer = 7(C)2*4(C)1*3(C)1*2(C)1

Now multiply and solve.. Here C is the Combination...

Answer 2

and to further clarify...
the combination "7 choose 2" is: 7(C)2 = 7!/(2!(7-2)!)

but I couldn't put it together right until you laid down the structure.

Answer 3

how do i input this on a calculator?

Answer 4

Do you have a calculator which directly finds for combinations???

Answer 5

See, the formula to solve is:

\[^nC_r = \frac{n!}{(n-r)! \times r!}\]

Can you solve it now??

Answer 6

1008

Answer 7

thanks buddhababy! (: & thanks guys for helping me out!

Answer 8

For example I do first one for you and rest you will do..
\[^7C_2 = \frac{7!}{(7-2)! \times 2!} = \frac{7 \times 6 \times 5!}{5! \times 2!} = \frac{7 \times 6 \times \cancel{5!}}{\cancel{5!} \times 2!}\]

So, \[^7C_2 = 7 \times 3 - 21\]

Now find the other values..

Answer 9

In place of - it will come =....

Answer 10

and I did not get 1008

Answer 11

Yeah I too got a different answer...