Question 1 Prove the following statements using mathematical induction. (a) 2" <(n + 2)! for all integers n21. (b) (1+2+

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Question 1 Prove The Following Statements Using Mathematical Induction A 2 N 2 For All Integers N21 B 1 2 1 (33.28 KiB) Viewed 23 times

Question 1 Prove the following statements using mathematical induction. (a) 2" <(n + 2)! for all integers n21. (b) (1+2+...+ n)' =' +2' +...+ n' for all n 21. (Remember that 1+2+...+n= n(n+1) ) 2 (c) n'+(n+1) + (n + 2) is divisible by 9 for all n 20. Question 2 In how many ways can one (a) arrange k people in a row? (b) form a row of 6 people from 10 people? Question 3 In how many ways can you choose (a) a soccer team (11 players) from 20 people (10 men and 10 women)? (b) and if the team must contain exactly 6 men? (c) and if the team must contain at least 2 men? Question 4 (a) How many "words" (strings) of length 10 are there over an alphabet of 26 letters? (b) How many ways to arrange the letters aabbccddd ?