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  3. 4 consider a chessboard shown below at starting at the...

Question: 4 consider a chessboard shown below at starting at the...

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4. Consider a chessboard, shown below. At starting at the square al (the lower right hand corner), you can go one step up or one step right at each move. The procedure stops until the point h8 (the upper right corner) is reached. a) How many different paths from al to h8 are possible? (b) How many differnt paths from al to h8 are possible if each path must pass through the square e4? 5. If 10 new teachers are to be divided among 5 schools, how many divisions are possible? What if each school must receive exactly two teachers?
1. (a) How many different 6-place license plates are possible if the first 3 places are letters and the other three are digits? (b) Repeat part (a) under the assumptions that no letter or number can be repeated in a single license plate (c) Repeat part (a) under the assumption that exactly one of the letters must be a Q. (a) In how many ways can 4 boys and 4 girls sit in a row? (b) In how many ways can 4 boys and 4 girls sit in a row if the boys and the girls are each 2. to sit together? (c) In how many ways if only the boys must sit together? (d) In how many ways if no two people of the same gender are allowed to sit together? 3. In how many ways can 8 people be seated in a row if (a) there are no restrictions on the seating arrangement? (b) persons A and B must sit next to each other? c) there are 4 married couples and each couple must sit together?
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