TheMathWorld

Problem – 12 How many solutions are there to the equation? x1+x2+x3+x4+x5=23, where xi, i=1, 2, 3, 4, 5, is a nonnegative integer such that a) x1≥1? b) xi≥1 for i=1, 2,…

Problem – 11 How many ways are there to assign three jobs to nineteen employees if each employee can be given more than one job?   Solution: Different ways to assign three…

Problem – 10 In how many different ways can nine elements be selected in order from a set with four elements when repetition is allowed?   Solution: Different ways to select…

Problem – 9 What is the coefficient of  in ?   Solution: Binomial theorem for (x+y)n = nC0xny0 + nC1xn-1y1+ nC2xn-2y2 + nC3xn-3y3 +…………+ nCn-1x1yn-1+ nCnx0yn Using the Binomial theorem,…

Problem – 8 Find the coefficient of in .   Solution: Binomial theorem for (x+y)n = nC0xny0 + nC1xn-1y1+ nC2xn-2y2 + nC3xn-3y3 +…………+ nCn-1x1yn-1+ nCnx0yn Using the Binomial theorem, coefficient…

Problem – 7 Nine women and five men are on the faculty in the mathematics department at a school. a) How many ways are there to select a committee of four members of…

Problem – 6 A club has 45 members. a) How many ways are there to choose four members of the club to serve on an executive committee? b) How many…

Problem – 5 How many bit strings of length 13 have a) exactly three 0s? b) more 0s than 1s? c) at least ten 1s? d) at least three 1s?   Solution:…

Problem – 4 In how many different orders can eight runners finish a race if no ties are allowed?     Solution: Number of possible orders are = 8! = 40320

Problem – 3 How many strings of six uppercase English letters are there a) if letters can be repeated? b) if no letter can be repeated? c) that start with Y,…