Math121 Discussion - 7th week solutions

Math121 Discussion - 7th week solutions - 5 4 3 = 360...

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MATH 121 DISCUSSION WEEK 7 WORKSHEET 1) (a) 8 possible pizzas: { } (no toppings), { P } , { S } , { GP } , { P, S } , { P, GP } , { S, GP } , { P, S, GP } (b) 2 n possible pizzas 2) (a) 11 (b) 59 (c) 20 (d) 49 (e) 26 3) (a) 30 (b) 30 4) (a) Draw one node with 3 branches coming out of it. From each of the 3 new nodes at the end of each branch, draw 2 branches going out of each node. You will now have 6 new nodes. Out of each of these 6 nodes, draw 2 branches. You should end up with 12 nodes at the very end. (b) 3 × 2 × 2 = 12 possible ways to fulfill the three requirements. (c) 3 × 2 × 2 × 5 = 60 possible ways to fulfill the four requirements. 5) (a) 6 × 6 × 6 × 6 = 6 4 = 1296 possible sequences. (b) 6 ×
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Unformatted text preview: 5 4 3 = 360 possible sequences . Think of it this way: on the rst roll, there are 6 possible numbers you could roll. If a number is not to be repeated in the sequence, then on the second roll, you cant get the number you rolled the rst time this reduces your possibilities for the second roll to 5 numbers. Likewise, on the third roll, there are only 4 possible choices if you are not to repeat the numbers you rolled during the rst two rolls. We can continue in this fashion. 6) 30 29 28 = 24,360 possible 1st, 2nd, 3rd place nishes. 1...
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