Question

At a family gather, 23 people are trying to fit into several cares. your car holds 6 people. How many different groups of 6 could you take in your car? I got 19769460480..is that right O.o?

Answer 1

You're choosing 6 from 23, so 23 choose 6 or 23c6

Answer 2

23*22*21..etc till 6 numbers down multiplied together?

Answer 3

My browser crashed... :'(

Answer 4

Okay, so that'll make:

\(\Large \color{Black}{\Rightarrow {23! \over (23 - 6)! \times 6!} }\)

\(\Large \color{Black}{\Rightarrow {23! \over 17! \times 6!} }\)

\(\Large \color{Black}{\Rightarrow {23 * 22 * 21 * 20 * 19 * 18 \over 6!} }\)
17! got cancelled.

\(\Large \color{Black}{\Rightarrow {23 \times 22 \times 21 \times 20 \times 19 \times 18 \over 6 \times 5 \times 4 \times 3 \times 2} }\)

Answer 5

Now a calculator :P

Answer 6

I got like 395 billion O.o

Answer 7

I got 100,947 on the calculator.

Answer 8

Do you have nCr function on your calculator?

Answer 9

Or wait http://www.wolframalpha.com/input/?i=23c6

Answer 10

that's what I used although i didn't know oyu could do that... Now I'm just wondering why when i entered it manually I got a different answer O:

Answer 11

Lol wolfram is the best

Answer 12

yea, definitely :P

Answer 13

Lol nice