"unit four~ permutations, combinations & the binomial theorem review 16. How many different 4-letter arrangements are possible using any 2 letters from the word SMILE and any 2 letters from the word FROG? (PC2.3) PCBT 4 Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers). PCBT 4.5 Expand, using the binomial theorem, ( x + y)" . 17. Find the value of a if the expansion of ( 2x + 3) 2975 has 18 terms. (PC4.5) Remember: *+ y' - - > has 2 terms (x+ y): - - > has 3 terms (x- yl. - > has 4 terms Use the following information to answer the next question. A student made the following statements regarding the expansion of ( a + b)4 . Statement 1 The total number of terms is 5. Statement 2 The middle term is 6ab? . Statement 3 The sum of the leading coefficients of all the terms is 14. Statement 4 For the term 4a b , the value of m is 1. Statement 5 The leading coefficient of the first term is 4 C, . 18. The three statements that are true are numbered , and (PC4.5) PCBT 4.6 Determine a specific term in the expansion of ' xy". 19. Determine the simplified form of the sixth term in the expansion of ( a - 2b). (PC4.6) the = Gx" y for x+ y -5- Math 30-1