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Practice A. It is now your turn to create your own. Start coloring/shading selected blocks in your Pascal's triangle. What pattern/object did you form? B. Use your Pascal's triangle to expand the following binomials. Binomial Expansion 1 . ( c + d ) ; 2. (3m - n) 3. (p + 3t) 4. (2r -3s) 5. How many Determine the binomial for expansion with the given situation below. terms are there in the 1. The literal coefficient of the 5th term is xy. expansion? 2. The numerical coefficient of the 6" term in the expansion is 243. 3. The numerical coefficient of the 2nd term in the expansion is 3840. Explain below how you got your answer. C. Determine the pattern and find out the number/figure which will complete the sequence. Explain your answer. 1. 58, 68, 57, 67, 56, a. 66 b. 55 c. 69 d. 54 2. 3, 4, 6, 10, 18, a. 26 b. 34 c. 36 d. 44 3. 10, 54, 98, 1312, 1716, a. 1720 b. 2020 c. 2130 d. 2120B. Assuming that all the players in men's basketball team can play any position, in how many ways can a group of five players be chosen from a team of 15 players? 1. This problem is a combination of. - players, taken at a time. 2. Using the truncated Pascal's triangle, you will go to Row because 3. Horizontally, you will stop at column. - because 4. The number of possible combination is. 5. Check your answer by using the formula/calculator. In a related note, Pascal's triangle can also show us the number of ways heads and tails can combine in a number of coin tosses. Therefore, Pascal's triangle can show us the probability of any combination. Practice Use the Truncated Pascal's Triangle or your calculator to solve the combination problems below. 1. In how many ways can a statistics teacher form a group of five students each from the class of 21 students? Show your substitution to the formula. 2. Complete Table 1. You may refer to Table 2 for reference. No. of No. of ways the Verification Coins Head Tail combination will Probability of possible happen combination: 0 tail (22 = 4) 2 1 tail 2 tails (25 = 32) 5 heads 4 heads 5 3 heads 2 heads 1 head 0 head Table 1 Pascal's Triangle: Combination and Probability MATHEMATICAL TRIPS IN THE MODERN WORLD 13 3. What is the probability of getting: a. exactly 4 heads or 4 tails? b. exactly 2 heads and 3 tails? c. exactly 1 head and 4 tails? d. exactly 5 heads? e. at most 3 heads? f. at least 3 heads