Question

In the Choose Four lottery game, players choose four different numbers from 1 to 15. The order of the numbers matters, so the selection of 4-15-6-3 is different form 6-4-15-3. (1).How many possible lottery sequences are there?

Answer 1

If the order matters, you use permutations.
If the order doesn't matter, you use combinations.

Answer 2

You will use permutations here.
In this case, you'll use 15p4 okay?

Answer 3

Wait what is permutations.

Answer 4

In general -

\(\Large \color{MidnightBlue}{\Rightarrow nPr = {n! \over (n - r)!} }\)

Answer 5

Oh I did something like that I'm going to draw it.

Answer 6

P=n!/(n-r)! 15x14x13x12x11x10x9x8x7x6x5x4x3x2x1

Answer 7

Yeah.

Answer 8

In the same way,


\(\Large \color{MidnightBlue}{\Rightarrow _{15}P_{4} = {15! \over (15 - 4)!} }\)

Answer 9

\(\Large \color{MidnightBlue}{\Rightarrow {15! \over 11!} }\)

\(\Large \color{MidnightBlue}{\Rightarrow 15 * 14 * 13 * 12 }\)

Answer 10

and so on and so on right

Answer 11

Yeah.

Answer 12

so 180 x 182= 32,760

Answer 13

Is that the answer in all together?