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Midterm Practice

# Midterm Practice - 1 In the expansion of(x y 2z)6 what is...

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1. In the expansion of ( x + y + 2 z ) 6 what is the coefficient in front of the term x 2 yz 3 . 2. Starting from a point ( a, b ) you may move to the point ( a + 1 , b + 1) or ( a + 1 , b - 1). In other words as you move one to the right you must move either up one or down one as well. Starting from the point (0 , 0) how many different paths are there to the point (10 , 6)? Starting from the point (10 , 6) how many paths are there that reach the point (100 , 40) that also go through a point ( n, 0) for some 10 < n < 100. 3. In an Urn there are 3 black balls numbered 1 to 3, 3 white balls , numbered 4 to 6 and 3 red balls, numbered 7 to 9. How many different 6 digit numbers can be formed in this way by using the digits on all possible selections of 2 black balls, 2 white balls and 2 red balls. 4. In a 10 digit number each digit is one of the digits 1 to 9. How many such numbers are there if the digit 3 occurs exactly 4 times? 5. In a hand of bridge what is the chance that your partner has exactly 4 spades given that you have exactly 6 spades?

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