BINOMIAL COEFFICIENTS (20 pts)
1. Expand the (2π β 2π)3 using binomial coefficient. (14 pts)
2. Find for the coefficient of a5b5; (a - 4b )10 (3 pts)
3. Find the 5th term after expanding the expression (3x β 4y)15 (3 pts)
PIGEONHOLE PRINCIPLE
Show that in a group of 27 English words, there must be at least two that begin with the same letter. (5 pts)
Solution.
1.
2.
Answer.The coefficient of -258048.
3.
The 5th term after expanding:
PIGEONHOLE PRINCIPLE
The pigeonhole principle states that if n items are put into m containers, with n>m, then at least one container must contain more than one item. We have n=27 English words and m=26 English letters. n>m,27>26, there are at least two words that begin with the same letters.
Comments