Question

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?

Answer 1

1:

There are 26 letters and 10 digits.

(a)

Each of the letter can be filled in 26 ways and each digit can be filled in 10 ways. So possible number of number plates is

26*26*26*10*10*10=17,576,000

(b)

First can be filled in 26 ways, second in 25 ways and third in 24 ways. Likewise digits can be filled in 10, 9 and 8 ways.

So possible number of number plates is

26*25*24*10*9*8=11232000

(c)

Number of ways of selecting place for Q out of three is C(3,1)= 3. Rest two letters can be filled in 26 ways each. So possible number of number plates is

3*26*26*10*10*10 = 2028000