Question

ihmih * B3 & MP3 Quiz 6 (MA275 - W20) 1. List all the 2-permutations and 2-combinations of {a,b,c,d,e}. 2. How many numbers must be selected from the set {1,2,3,4,5,6 } to guarantee that at least one pair of these numbers add up to 7? 3. What is the coefficient of in (1 + x)"l? 4. A passcode consists of five digits. Since this is a passcode, the order in which the digits appear matters. answer the following questions. 1) number of possible passcodes if the last digit is odd 2) number of possible passcodes if the first digit is not zero 3) number of possible passcodes if the last digit is odd and the first digit is not zero

Answer 1

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ni The number of permutations of n object , token k at a time is given by the ratio (n-k)! Here 0 = 5 K= 2 {a,b,c,d,e} n=5 5YUX : No.of Peomectations = = = 120 (5-2)! The neember of distinct combination of n objecti , token k at a time is given by ratic n ki (n-k)! No. of combinations - 5! 5XXX! 2! (5-2)! = 2128 - To] {a,b,c,d, eg .: List of au 2- Permutatione are ab ac ad ca ea сь eЬ cd ea be bd be db do de . list of all 2- combinations are about ac tad. ae bc bd be D2 d