Who is asking: Student
Level: All

Question:
Hmm....I'm asking a question about Finite.

the question is :

How many three-digit numbers can be formed using only the numbers 1 to 7 if the number 2 must be included??

Thanks for teaching me this question, please reply the procedre to me!!

You may find it easiest to look at the problem in parts - count the number that you want that use 3 - 2's; 2 - 2's; and 1 - 2.

3 - 2's has only one possibility -- 222

2 - 2's has to broken down into 2 2 _, 2 _ 2, or _ 2 2 where the blank can be any one of the other 6 numbers from 1 to 7 (2 is excluded). This gives 6+6+6=18 possibilities.

1 - 2's has to broken down into 2 _ _, _ 2 _, or _ _ 2 where each blank can be any one of the other 6 numbers from 1 to 7 (2 is excluded). This gives 6x6 =36 ways in each of the 3 cases for 36+36+36= 108 in all.

In total there are 1 + 18 + 108 = 127 possibilities.

Cheers,
Penny