1 a combination lock will open when you select the right...

1. A combination lock will open when you select the right choice of four numbers (from 1 to 40, inclusive). How many different lock combinations are possible? 2. In how many orders can five girls and three boys walk through a doorway single file for each of the following? a) There are no restrictions b) The boys walk before the girls 3. From a pool of 16 candidates, the offices of president, vice-president, secretary, and treasurer need to be filled. In how many different ways can the offices be filled?

Transcript

00:01 Okay, the first question, your lock has four numbers and each number can be either, one, two, three, four up to 40.

00:10 So, first place, 40 choices.

00:14 Second place, 40 choices and so on.

00:18 Each place, you have a choice of 40 numbers.

00:22 So that would be 40 power of four, which you can work out on a calculator.

00:33 It's 256 ,000 ,000, so 2 ,500 ,000 different combinations are possible.

00:47 Okay, question two, we have five girls and three boys going through a door.

00:53 How many ways can this be done? well, i don't care if this boy or girl, then the first person going through, there will be eight choices.

01:01 Then 7, then 6, and so on, all the way down to 1.

01:08 And that is 8 factorial.

01:11 If you can work out on a calculator, the ti84 plus, you press the math button, go across to the prob menu, and go down to item 4 factorial, and then you can simply work out the result that way.

01:34 And the answer you should get is 4 -0 -3 -2 -0.

01:43 Now, if you are told the boys must go in first, then things will change.

01:50 The three boys go in first, three times two times one, different ways.

01:57 So six ways for the boys to go in.

02:00 The girls then will be five times four times three times two times one.

02:06 So it's 3 a factorial times 5 factorial.

02:11 And here we can do it actually manually.

02:15 Here we have 6 and 5 times 4 is 20 times 6...