Question

PartB (COMBINATORICS) -LEAVE ALL ANSWERA IN TERMS OF C(n,r) or factorials, Q4(a)(i ) In how many ways can you arrange the letters in the word INQUISITIVE? in how many of the above arrangements, U immediately follows Q? Q4. (b)Su next semester. Your favorite professor, John Smith, is teaching 2 courses next semester and therefore ppose you are a math major who is behind in requirements and you must take 4 math courses you "must" take at least one of them. If there are 8 different math courses (besides those that John Smith is teaching) available to you, how many ways are there to take your 4 classes? Show all work with full explanation Hint: Consider cases that you either take one or two courses with Prof. Smith. Q4(c) The number of ways of distributing 12 identical bottles of lemonade to 5 children, such that each child gets at least one bottle. Write the formula that you are using Q4d) Give a combinatorial argument to prove the following identity. Give a word problem which can be done in two ways; for one solution the answer is the right hand side and for the second solution the answer is the left hand side of the following equation. Q5(a) Model the following problems as a specified coefficient of an exponential generating function. Start with an equation, explain all variables. Find the exponential generating function in simplified form. Give the generating function in simplified form and say which coefficient we are looking for Do not calculate the coefficient. How many n-digit sequences (from the alphabet (0,1, 2,3) are there if 1 and 3 occur an even number of times? Hintl Let e,- the of times the digit i is used; i 0,1,2,3)

Answer 1

Part B l0l =10 3 (b) Take - 3 ren . Ahibule 다 41刊4TH 2 아n saML