= 39916800/8
= 4989600
b) How many of these start with the letter M?
A=2
T=2
=10!/2!2!
= 3628800/4
= 907200
c) How many of the arrangements in part (a) have the T’s together?
M=2
A=2
T’s together =1
=10!/2!2!
= 3628800/4
= 907200
4

8)
We could solve this question using combination, because the order does not
matter. 9C3 is equivalent to considering permutations with repeated items, because
Ncr= n!/(r!)(n-r)!, therefore 9C3 can be written as 9!/(3!)(9-3)!= 84 and 9!/(3!)(6!) also
equals to 84.
9 a) How many different ways can be the parents be chosen for the small
group?
8C3 = 56
b) How many ways can the students be chosen for the large group if Stefan
and Dylan must be in the small group?
41C30 = 3.16 x 10^9
c) How many ways can the groups be arranged if Reena and both her parents
must be in the small group?
We need 30 kids out of the 42 who are left and 5 out of the 6 parents that are left.
42C30 x 6C5 = 6.63478 x 10^10
10 ) Simplify each expression and write it without using factorial notation.
a)
(n+4)!/ (n+2)!
= (n + 4) (n+3) (n+2) (n+1)n … 3 x 2 x 1/(n+2)!
= (n+4)(n+3)(n+2)! / (n+2)!
= (n+4)(n+3)
b) (n-r+1)!/(n-r-2)!
=
(n-r+1)(n-r)(n-r-1)(n-r-2)!/ (n-r-2)!
=
(n-r+1)(n-r)(n-r-1)
5

11)
The lottery competition
that I investigated was OLG lotteries: Lotto max, they
have a 25 million jackpot. Eah $5 play gives you 3 lines. Which means you have 3
chances to win. Each line gets you 7 numbers between 1-50. For the first line you
can choose the numbers yourself or have quickpick select for you (random number
generator). However you pick the first line the next two are randomly generated. No
matter what numbers are chosen they all have equal chance of winning. Match all 3
in a line you win a free play. If you match all 7 in a line you win the jackpot.
To calculate the number of combinations when picking 7 numbers out of 50 we
would use the equation 50C7 which gives us 50!/(7!)(50-7)!= 99884400 different
combinations for those 7 numbers. This means that the probability of winning is very
small. Each ticket itself has 1 in 7 odds of winning. Since the ticket costs $5 and
there are 99884400 combinations and the odds of winning are small I conclude that
the prizes offer are not fair and its not worth playing. I think people
continue to play
because they are attracted to the big prizes but some also play just for fun.
6

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- Spring '19
- Committee, The Jackpot, Red Stripe, 72C6