Professor Smit has prepared a total of 11 question for his s

Professor Smit has prepared a total of 11 question for his second exam. Five of these question are easy. two are hard , and four are moderately difficult.

1) how many ways are there to select the first question ,if it can be any of the available 11 question ?

2) How many ways are there to select question number 1 and question number 2 if the professor wishes both of those to be moderately difficult ?

3) How many ways are there to number the question from 1 to 11 ( without repeating number) , if all the easy question precede all the moderately difficult question ,which in turn precede all the hard question ?

4) how many ways are there do number the question from 1 to 11 (without repeating numbers), if none of the first these question may be hard ?

5) how many ways are these to number the question from 1 to 11 (without repeating numbers ) if none of the last three question may be easy ?

6) Professor smit is wondering how to order the moderately diffcult question in the problem set . how many arrangement of these four question are possible ?

7) how many ways are there to select these three question of one of them has to be easy, one hard , and one moderately difficult ?

Solution

1) 11c1 as one question has to be selected from 11.

2)4c1*3c1 as after chossing one question the number of question with moderately difficult will be 3

3)5c1*4c1*3c1*2c1*1c1*4c1*3c1*2c1*1c1*2c1*1c1 as for first five only 5 question available. next 4 only 4 choice and last two only 2 choices.

4)9c1*8c1*7c1*8c1*7c1*6c1*5c1*4c1*3c1*2c1*1c1

6)4!

7)5c1*4c1*2c1