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mdm12Section4_R_OddSolutionsFinal

mdm12Section4_R_OddSolutionsFinal - 1260 n = = c If you end...

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Q1 Q3-9 Q11-13 Q15 CHAPTER 4 Review of Key Concepts, p. 260 Solutions to Odd Number Problems 1. Top

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3 n (no restrictions) = 6! = 720 n (tallest and shortest together) = 5!2! = 240 n (tallest and shortest apart) = 720 – 240 = 480 5. n 2 n n ! 0 1 1 1 2 1 2 4 2 3 8 6 4 16 24 For 0 n 3, n ! < 2 n . 7. n = 12 P 3 = 1320 9. a) There are two bs, two as, and two ls. 8! 2!2!2! 5040 n = = b) If you begin with the letter a , there are seven more letters to arrange, two pairs of which are identical. 7! 2!2!

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Unformatted text preview: 1260 n = = c) If you end with the letter e, there are 7 more letters to arrange, three pairs of which are identical. 7! 2!2!2! 630 n = = Top 11. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 13. Pattern 1: Each term is the sum of the two terms above it. Pattern 2: Sum of 1st row = 2 Sum of 2nd row = 2 1 Sum of 3rd row = 2 2 Sum of 4th row = 2 3 Sum of n th row = 2 n-1 Pattern 3: The numbers in each row are symmetric about the centre. Top 15. Top...
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