4. A group of 5 grade 1 1 students and 16 grade 12 students apply to go to a student conference in Vancouver, but there is only enough funding to send 6 students. a) Determine how many ways the 6 students can be selected if equal numbers of grade 11's and grade 12's are chosen? /1 b) Determine the number of groups that can be created if at least three of f4 the students must be in grade 12? Solve this problem using 2 different methods. c) Determine the probability that the group of 6 students sent to Vancouver would consist of no more than 2 grade 12 students. f2 5. Lotto 6/49 is a Canadian lottery game where you select a certain combination of 6 numbers from 1-49 to earn a chance at winning a cash prize. There are no repetitions of numbers here. Additionally, you must select a bonus number. There are certain cash prizes you can win that depend on how many correct numbers you select on your ticket. Here is an example of the prize breakdown of the main draw from Saturday, January 16, 2021: LOTTO 6/49 Prize Breakdown Saturday, January 16, 2021 Jackpot: $5,000,000.00 MAIN DRAW Bonus 9 10 21 28 35 43 34 Prize Category Winners Prize 6 of 6 CARRIED OVER 5 of 6 + Bonus 0 NOT WON 5 of 6 80 $2, 157.50 4 of 6 1,105 $79.90 3 of 6 77,169 $10.00 2 of 6 + Bonus 48,353 $5.00 2 of 6 530,406 FREE PLAY GUARANTEED PRIZE DRAW Prize Breakdown Exact Match Only Winning Number Winners Prize 48396220-01 1 - Ontario $1,000.000.00 EXTRA Prize Breakdown Saturday, January 16, 2021As you can see, there are seven prize categories: 1. 6 of6 {you selected all 6 numbers correctly} 5 of 6 + bonus {you selected 5 of 6 numbers correctly and the bonus} . 5 of 6 {you selected 5 of 6 numbers correctly} . 4 of 6 {you selected 4 of 6 numbers correctly} 3 of 6 {you selected 3 of 6 numbers correctly} . 2 of 6 + bonus {you selected 2 of 6 numbers correctly and the bonus} . 2 of 6 {you selected 2 of 6 numbers correctly} a) Is this lottery an example of a permutation or a combination? Explain. f] b) If you purchased one Lotto 6149 ticket, determine the probability that you would win the main prize \"6 of 6"? Leave your answer as a fraction. / l c) If you purchased ten Lotto 6M9 tickets, determine the probability that you would win the main prize \"6 of 6\"? Leave your answer as a fraction. / l d) If you purchased one Lotto 6X49 ticket determine the probability that you / 1 would win the prize \"5 of 6\"? (Hint: To match 5 winning numbers you must select 5 of 6 winning numbers AND you must select 1 number from the other 43 non-winning numbers.)