MATH
Math121 Discussion - 7th week solutions

# Math121 Discussion - 7th week solutions - MATH 121...

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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 ﬁrst 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 can’t get the number you rolled the ﬁrst 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 ﬁrst two rolls. We can continue in this fashion. 6) 30 × 29 × 28 = 24,360 possible 1st, 2nd, 3rd place ﬁnishes. 1...
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