Subject: Engineering Data Analysis

Please answer all the questions:

1. (Show your solutions)

In how many ways can 3 boys and 3 girls be seated at a round table if

a.without restriction

b2 particular people must not sit next to each other

c. boys and girls are alternating

2. (Show your solutions)

(a) How many four-digit numbers can be formed from the digit 0, 1, 2, 3, 4,5, 6, 7, 8 ,9 if each digit can be used only once

(b)from part (a) How many of these are even numbers?

(c) from part (a) ,How many of these are greater than 3,500?

3. (Show your solutions)

Six cards are drawn from a deck of playing cards find the number of ways of selecting

a.all cards are of the same suit (ex. 6 diamond cards)

b.at least 3 face cards

c.at most 3 red cards

4. (Show your solutions)

Marlon works at the local museum. He has 10 pieces of art to choose, but he can only hang 4 of the frames. How many possible ways can Marlon choose and then arrange four frames?