Discrete Mathematics Answers

Out of 300 students taking discrete mathematics, 60 take coffee, 27 take cocoa 36 take tea, 17 take tea only, 47 take chocolate only, 7 take chocolate and cocoa ,3 take chocolate, tea and cocoa ,20 take cocoa only ,2 take tea, coffee and chocolate, 30 take coffee only, 9 take tea and chocolate whereas 12 take tea and coffee . Express this information on a venn diagram.

What is the coefficient of x^3 y^13 in the expansion of (−1x+2y)^16?

What is the coefficient of x^3 y^13 in the expansion of (−1x+2y)^16?

Find the coefficient of x^5 in (1+x)^11.

How many ways are there to select 9 countries in the United Nations to serve on a council if 1 is selected from a block of 50, 2 are selected from a block of 67 and 6 are selected from the remaining 72 countries?

Suppose that a department contains 8 men and 20 women. How many ways are there to form a committee with 6 members if it must have strictly more women than men?

15 players for a softball team show up for a game:

(a) How many ways are there to choose 10 players to take the field?
10!/(5!)


(b) How many ways are there to assign the 10 positions by selecting players from the 15 people who show up?


(c) Of the 15 people who show up, 5 are women. How many ways are there to choose 10 players to take the field if at least one of these players must be women?

How many bit strings of length 14 have:

(a) Exactly three 0s?
(b) The same number of 0s as 1s?
(d) At least three 1s?

Find the value of each of the following quantities:
C(8,4)=

C(12,7)=

C(12,8)=

C(11,1)=

C(10,9)=

C(8,6)=

This question concerns bit strings of length six. These bit strings can be divided up into four types depending on their initial and terminal bit. Thus the types are: 0XXXX0, 0XXXX1, 1XXXX0, 1XXXX1.
How many bit strings of length six must you select before you are sure to have at least 6 that are of the same type? (Assume that when you select bit strings you always select different ones from ones you have already selected.)