Subject: Probability and Statistics

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A.

Solve the following problems. 1) How many chords can be drawn given 6 points on a circle? 2) The figure below shows 5 vertical lines and 4 horizontal lines which intersect forming right angles. As a result, rectangles are formed. How many rectangles in all are formed?1. Which of the following situation does not require combination? A. Forming a committee of councilors. B. Assigning rooms to conference participants. C. Selecting the top 3 winners in a singing contest. D. Choosing two literature books to buy from a variety of choices. 2. Which of the following requires combination? A. Issuing plate numbers. B. Lining up in paying bills. C. Arranging 6 people in a round table. D. Choosing five badminton players from 12 athletes. 3. Electing an auditor and a treasurer from 8 candidates is an example of A. Permutation B. Combination C. Sets D. cannot be determined 4. The number of combinations of n objects taken r at a time is denoted by B. n! n! D. n! (n-r)ir! C. (n-n)r! 5. Evaluate: 1263. A. 2,200 B. 1,320 C. 220 D. 132 6. How many straight lines can be drawn using five points (A, B, C, D, and E), in which no three points are collinear? A. 0 B. 5 C. 6 D. 10 7. In a box, there are 5 black pens, 3 white pens and 4 red pens. In how many ways can 2 black pens, 2 white pens and 2 red pens be chosen? A. 19 B. 30 C. 38 D. 180 8. How many diagonals can be drawn in a 9-sided polygon? A. 72 B. 36 C, 27 D. 12 For items 9 - 12. A group of 6 women and 9 men will form four-person committees. How many committees are possible if it must consist of the following: 9. 2 men and 2 women? A. 51 B. 102 C. 540 D. 1,365 10. at most 3 men? A. 180 B. 504 C. 1,224 D. 1,239 1 1. a majority of women? A. 15 B. 180 C. 195 D. 2,70012. minimum of 2 women? A. 126 B. 735 C. 1,044 D. 1,365 13. There are 7 dots randomly placed on a circle, how many triangles can be formed using the dots as vertices? A. 7 B. 20 C. 35 D. 84 14. There are 13 volleyball teams during the 2019 CARAA. How many games must be played in order for each team to play every other team exactly once? A. 13 B. 26 C. 78 D. 286 15. Fifteen participants for the MTAP competition were asked to shake hands and introduce themselves with each other. How many handshakes took place? A. 15 B. 30 C. 45 D. 1051) A dance instructor asks each student to do 4 out of the 10 dance routines. Of the 10 dance routines, 2 are easy, 5 are moderately difficult and 3 are difficult. In how many ways can a student select each of the following for the 4 dance routines? a. 4 moderately difficult routines b. 2 moderately difficult and 2 difficult routines c. 1 easy and 3 difficult routines 2) From a deck of 52 playing cards, 5 cards are to be drawn. How many sets of 5 cards are possible if: a. there is no restriction? b. there are 2 aces and 3 jacks? c. all cards are black? d. all cards are diamonds? e. there are 3 face-cards, 1 king, and 1 spade