Math 106, Quantitative Reasoning, Test 3

How many counting numbers have five distrinct nonzero digits such that the sum of the five digits is 15

1. Count the number of sets of five nonzero digits (1-9) that sum to 15. Notice that 1+2+3+4+5=15. Are there any more such sets? (no) 2. Which of the following should be used to count the number of was arrange 5 distinct digits? (permutations) 3. Use formula [nPr=n!/(n-r)!], where n=5 and r=5 4. 5p5 = 5!/(5-5)! = 5!/0! = 5! = 120

Counting numbers are to be formed using only the digits 1,2,3,4,5,7,8, and 9. Determine the number of different possibilities for two-digits numbers.

1. count the total number of digits being used (5) 2. For the first digit, how many choices are there. (5) 3. For the second digit in number, how many choices are there? (5) 4. Recall the fundamental counting principle. When a task consists of k seperate parts, if the first part can be done in n_1 ways, the second can be done in n_2 ways, etc throught the kth part, the total number of ways to complete the task is given by n_1(n_2)....(n_k) 5. Apply the fundemental counting principle to find the total number of two digit numbers that can be formed [5(5)=25]

The table below categorizes 25 senators by political party and gender. One member is chosen at random. In how many ways can the chosen person be a man or republican? Men Women t Dem 2 4 6 Rep 13 6 19 t 15 10 25

17 there are 13 men, and 6 democrats. Two of the men are democrates. 13+6-2=17

If a given set has 9 elements, how many of it's subsets have at most three elements?

Since there are at most three elements, then there can be either 0,1,2, or 3 elements per set. Since order does not matter, use combinations to determine the number of possible subsets. if there are 0 elements per set, find the number of combinations of 9 elements taken 0 at a time. 9_C_0=1 If there is 1 element per set, find 9_C_1 9_C_1=9 Find the remaining combinations. 9_C_2=36 9_C_3=84 Add the number of subsets for each possible number of elements per set. # of subsets= 9_C-0 +..... # of subsets= 1+9+36+84 # of subsets= 130

Anne Kelly randomly chooses a single ball from the can shown to the right. Find the odds against the event. red or yellow (R or Y) jar contents red=3 blue=4 yellow=4 total=11

The odds for finding are R+Y to T-(r+y) 3+4 to 11-(3+4) 7 to 4 Therefor, the odds against finding red or yellow is 4 to 7

A panel containing three on-off switches in a row is to be set. Assuming no restrictions on individual switches, use the fundamental counting principle to find the total number of possible panel settings.

[2][2][2]=2x2x2=8 Because: there are three switches ([][][]), and a switch only has two sides ([2][2][2]). Then you multiply those numbers, (8).

How many ways can a president, vice-president, secretary, and treasure be chosen from a committee of 6 people?

[6][5][4][3]=360

In how many ways could members of the following club line up all 7 members for a photograph? N={Jim, Alan, Tammy, Cathy, David, Sandy, Ashley}

[7][6][5][4][3][2][1]=5040

Find the number of distinguishable arrangements of the letters of the word CENTILLION

n!/ (k_1 k_2 k_3 ...) 10!/ 1! 1! 2! 1! 2! 2! 1! 453600