Question

discrete mathematics

a. 25 identical glass orbs are to be partitioned into 5 groups. How many ways are there to do this? b. The orbs are to be partitioned such that each group gets at least one orb. How many ways are there to this? 6 of the orbs are given to the 1 group. How many ways are there to partition the remaining orbs such that the first group has at least the 6 from the beginning of this statement, and the 5 C. group gets none? 9: In complete darkness, someone needs to reach into a chaotically arranged sock drawer to pull out a matching pair of socks. The drawer contains a vast plethora of black socks, white socks, grey socks, green socks, and red socks. 2 socks of a given color make a matching pair. a. Given that the individual cannot see into the drawer to ascertain which sock is which color, how many must be pulled from the drawer, at minimum, to guarantee at least one matching pair once the socks can be seen? b. c. How many must be pulled to guarantee at least one sock of each color, if there are 12 individual socks of each color inside the drawer? How many must be pulled to guarantee at least two matching pairs? 10: A specific state legislature contains 51 members. A select committee of 7 must be chosen. The chair of the committee will be the head of the legislature, and the vice-chair of the committee will be the head of the legislature's lieutenant. How many ways are there to complete the committee?

Answer 1

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