4th Edition Guide 4: Word Translations Chapter 4

[vivian_quaye]

Slot Method

Pg. 68 poses a sample poblem: An office manager must choose a 5-digit lock code for the office door. The first and last digits of the code must be odd, and no repetition of the digits is allowed. How many different lock codes are possible.

As per the book, I understand there are 5 different odd digits (1, 3, 5, 7, and 9) so there are 5 ways to get the 1st digit, leaving 4 ways to get the last digit. The book suggests 8,7,6 digits are left. Can someone confirm where the 8,7,6 choices came from?

Thank you.

[Ben Ku]

As per the book, I understand there are 5 different odd digits (1, 3, 5, 7, and 9) so there are 5 ways to get the 1st digit, leaving 4 ways to get the last digit. The book suggests 8,7,6 digits are left. Can someone confirm where the 8,7,6 choices came from?

Since no repetition of the digits are allowed, because two digits had already been used for the first and last slot, there are only 8 possible digits left for the second slot.

Likewise, after three slots have been filled, there are 7 digits left for the third, and 6 digits left for the fourth.

Hope that helps.

[koram]

As per the book, I understand there are 5 different odd digits (1, 3, 5, 7, and 9) so there are 5 ways to get the 1st digit, leaving 4 ways to get the last digit. The book suggests 8,7,6 digits are left. Can someone confirm where the 8,7,6 choices came from?

Since no repetition of the digits are allowed, because two digits had already been used for the first and last slot, there are only 8 possible digits left for the second slot.

Likewise, after three slots have been filled, there are 7 digits left for the third, and 6 digits left for the fourth.

Hope that helps.

Hi, my question is associated to the second slot, shouldn't it be 7 since the first and the last slots are already assigned? My reasoning is, since we cannot have repetition, and that the first number and the last number are already determined, by having the second number be 8, there could be a repetition of the last number.

Is it possible to explain why the second number is 8 instead of 7?

Thank you

[Ben Ku]

Hi, my question is associated to the second slot, shouldn't it be 7 since the first and the last slots are already assigned? My reasoning is, since we cannot have repetition, and that the first number and the last number are already determined, by having the second number be 8, there could be a repetition of the last number.

Is it possible to explain why the second number is 8 instead of 7?

Thank you

There are a total of TEN digits:
0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Since the first and last slot are taken, only EIGHT possible digits remain.

Hope that makes sense.