Guide 4: Word Translations, 4th Ed., Ch 4, #4 (Pg.75)

[alanfong31]

Hi Instructors,

I am confused with the strategy/explanation for problem #4. I understand that we would use the slot method.
P75#4
1) 4 _ _ _ 3
2) 4 5 4 3 3

My question relates to the second portion of the explanation. Why do we use 5 instead of 6? Is it due to the fact we have 5 numbers left since we used 2 already?

If so I am confused with the example provided on Combinatorics Strategy - page 68, which was not apply. Why did we start with 8 rather than 7?

P68#Example Problem
1) 5 _ _ _ _ 4
2) 5 8 7 6 4

Based on the example, they started with 8 choices, rather than 7.

I am getting confused with the difference between these two problems. May you differential the two or am I missing something?

[StaceyKoprince]

When posting, please follow forum guidelines and post the text of the problem! We don't always have our books available when we answer questions!

In the first problem, the key is this language:
"with no repeated digits"
They tell us we can't repeat, so we do have to reduce the number of possibilities at step 2.

On the second problem, 8 is the right number when restricting the digits. There are 10 possible digits; don't forget about zero! Zero through nine = 10 digits. We've used two already, so that leaves 8 more to use at that point in the problem.