abrk for n N. It can be re-written as a (a + b) = (^) a...

 

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abrk for n N. It can be re-written as a (a + b) = (^) a brk f n k=0 ab, n! i!j!" The Trinomial Formula is then (a+b+c)": = ab, (i) a'b' c, with i, j, k 0 i+j+k=n (a+b) Recall the Binomial Formula == (;) i+j=n with i, j > 0 and n! n j and() = ilj!k! = A. Find the coefficient of xy 26 in the expansion of (2x-3y+22) 10. SHOW your work! B. Find the coefficient of 12 in the expansion of (3x-x + 1)10. SHOW your work! 2. (10 marks) Find the number of distinct ways of distributing 12 balloons to 7 kids if A. there are no restrictions B. each kid must get at least one balloon C. the oldest kid must get at least 2 balloons D. the oldest kid must get between 2 and 6 balloons E. the oldest kid must get 4 balloons or more, and the youngest kid must get 3 balloons or more. 3.(10 marks) Find the number of distinct bit strings of length 12 that have exactly 6 consecutive zero bits, or exactly 6 consecutive one bits, but not both. 4. (4 marks) How many ways are there to A. Rearrange the letters in the string HARDYHARHARHARDY B. Travel in 5-space vwxyz, from the origin (0, 0, 0, 0, 0) to the point (4, 2, 4, 2, 4) by taking steps one-unit in the positive v direction, one-unit in the positive w direction, one-unit in the positive direction, one-unit in the positive y direction and one-unit in the positive z direction. abrk for n N. It can be re-written as a (a + b) = (^) a brk f n k=0 ab, n! i!j!" The Trinomial Formula is then (a+b+c)": = ab, (i) a'b' c, with i, j, k 0 i+j+k=n (a+b) Recall the Binomial Formula == (;) i+j=n with i, j > 0 and n! n j and() = ilj!k! = A. Find the coefficient of xy 26 in the expansion of (2x-3y+22) 10. SHOW your work! B. Find the coefficient of 12 in the expansion of (3x-x + 1)10. SHOW your work! 2. (10 marks) Find the number of distinct ways of distributing 12 balloons to 7 kids if A. there are no restrictions B. each kid must get at least one balloon C. the oldest kid must get at least 2 balloons D. the oldest kid must get between 2 and 6 balloons E. the oldest kid must get 4 balloons or more, and the youngest kid must get 3 balloons or more. 3.(10 marks) Find the number of distinct bit strings of length 12 that have exactly 6 consecutive zero bits, or exactly 6 consecutive one bits, but not both. 4. (4 marks) How many ways are there to A. Rearrange the letters in the string HARDYHARHARHARDY B. Travel in 5-space vwxyz, from the origin (0, 0, 0, 0, 0) to the point (4, 2, 4, 2, 4) by taking steps one-unit in the positive v direction, one-unit in the positive w direction, one-unit in the positive direction, one-unit in the positive y direction and one-unit in the positive z direction.