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Magazine Problem 10
Find the number of terms in the expansion of each expression. \((x+y+z)^{10}\)
Problem 11
Find the number of terms in the expansion of each expression. \((w+x+y+z)^{12}\)
Problem 11
Ask about strings of length 5 formed using the letters ABCDEFG without repetitions. How many strings begin with the letter \(F\) and do not end with \(E B\) in that order?
Problem 11
Determine how many strings can be formed by ordering the letters ABCDE subject to the conditions given. Contains the letters \(A C E\) together in any order
Problem 11
An inventory consists of a list of 115 items, each marked "available" or "unavailable" There are 60 available items Show that there are at least two available items in the list exactly four items apart.
Problem 12
An inventory consists of a list of 100 items, each marked "available" or "unavailable." There are 55 available items. Show that there are at least two available items in the list exactly nine items apart.
Problem 12
Ask about strings of length 5 formed using the letters ABCDEFG without repetitions. How many strings contain \(C E G\) together in that order?
Problem 13
Find the next row of Pascal's triangle given the row $$\begin{array}{llllllll}1 & 7 & 21 & 35 & 35 & 21 & 7 & 1\end{array}$$
Problem 13
An inventory consists of a list of 80 items, each marked "available" or "unavailable." There are 50 available items. Show that there are at least two unavailable items in the list either three or six items apart.
Problem 15
Prove that $$\sum_{k=0}^{m}(-1)^{k} C(n, k)=(-1)^{m} C(n-1, m)$$ for all \(m, 0 \leq m \leq n-1\)
