These questions are from a grade 12, Data Management class. Any help would be great. I am completely stuck. Simple terminolgy in explaining would be useful The first two are more about being able to explain reasoning in words while the last two will involve calculations. Thanks to everyone.

1. Until 1997, most licence plates for passenger cars in Ontario had three numbers followed by three letters. Explain why the goverment began to increase the number of letters to four.

2. A hockey team consists of 17 players (9 forwards, 6 defensemen and 2 goalies). The starting line-up consists of 3 forwards, 2 defensemen and 1 goalie. Explain way the number of ways the players can be selected only is less than if they are selected to specific positions.

3. Six students are asked to secretly choose a number from 1 to 15. Determine the probability that at least two students choose the same number to the nearest thousandth.

4. A pizzeria offers 10 different toppings. A group of people plan to order six pizzas, with up to three toppings on each. They decide to order each topping exactly once and to have at least on topping on each pizza. Determine the different cases possible when distributing the toppings in this way and the number of ways that each can be done.

2. Originally Posted by crazy_gal108
These questions are from a grade 12, Data Management class. Any help would be great. I am completely stuck. Simple terminolgy in explaining would be useful The first two are more about being able to explain reasoning in words while the last two will involve calculations. Thanks to everyone.

1. Until 1997, most licence plates for passenger cars in Ontario had three numbers followed by three letters. Explain why the goverment began to increase the number of letters to four.
Let us determine the number of distinct codes formed.
You first have 3 numbers then 3 letters which is,
$10\cdot 10\cdot 10\cdot 26\cdot 26\cdot 26=17,576,000$
Apparently there were too many cars, by adding a forth letter gives,
$456,976,000$

3. Originally Posted by crazy_gal108

3. Six students are asked to secretly choose a number from 1 to 15. Determine the probability that at least two students choose the same number to the nearest thousandth.
Since we are talking 'bout thousands only the first three digits are important. Thus, all the numbers are,
Code:
1.000
1.001
1.002
........
14.998
14.999
15.000
To make the problem easier, let us do the opposite statement. Meaning, the probability that 6 students do not choose the same number and then from that subtract one.

There are a total of 14,001 numbers.

STUDENT1)Can chose any one thus probability is 1.

STUDENT2)Can chose any number except that of student1, thus the probability is $14000/14001$

STUDENT3)Can chose any number except that of student1 and student2 thus the probability is $13999/14001$

STUDENT4)Probability is $13998/14001$

STUDENT5)Probability is $13997/14001$

STUDENT6)Probability is $13996/14001$

Thus, the probability that they DO is,
$1-\frac{_{14000}\mbox{P}_{5}}{14001^5}$
Evaluating we find that,
0.0010709185167321222566663866769298
Is the probability thus,
a little more than 1%