Question

A lottery game asks you to pick six numbers from the range 1 through 40. How many ways are there to play this lottery game? Assume that this is a game where the order of your picks does NOT matter.

3,838,380

2,763,633,600

240

40
1 points
QUESTION 49

If we toss a pair of dice, what is the probability that a sum of 8 appears?

4 / 36

1 / 36

1 / 6

5 / 36

Answer 1

Hi @kittymeow101 !

Have you tried the first question?

Answer 2

no i dont understand it

Answer 3

Okay.

1. To play the lottery game you have to choose six numbers from the range 1 to 40.

Now, I am assuming that all these 6 numbers are distinct. Ok?

Answer 4

Now, basically, the question is a combination of 2 questions:

1.Choosing 6 distinct numbers from 1 to 40.
2. Arranging them in different patters.

Answer 5

1. How can we choose the 6 numbers? We use the cominatorics formula of combination.

\(\large{^nC_r}\)

Here, n = 40 and r = 6

Answer 6

Now, if order of the numbers was not important then \(\large{^{40}C_{6}}\) would have been the answer.

But, if the order of the numbers is important, then:

1. What are the possible ways of arranging 6 distinct numbers in 6 possible places?

\(\large{^6P_{6} = 6!}\)

2. Because our method is a combination of selecting AND arranging. Thus:

required answer = \(\large{6! * \ ^{40}C_{6}}\)

Now, `*` came because of the AND part.

Answer 7

Now, your job is to evaluate both the possibilities and see which one has is present in the option.