permutations: How many ten-digit codes can you create if....

i have a math question which i couldnt figure out, and i was wondering if anyone could help me...thanks!!

suppose you are designing a coding system for data relayed by a satellite. To make transmissions errors easier to detect, each code must have no repeated digits.

how many ten-digit codes can you create if the first three digits must be 1, 3, or 6?

Re: permutations

Hello, xo_caroline_xo!

Each ten-digit code must have no repeated digits.

How many codes can you create if the first three digits must be 1, 3, or 6?

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We are to arrange the ten digits: {0,1,2,3,4,5,6,7,8,9}.

The first digit must be 1, 3, or 6 . . . There are 3 choices.

Then the remaining nine digits can be arranged in 9! ways.

Answer: \(\displaystyle \,\)3 \(\displaystyle \times\) 9! \(\displaystyle \,\)= \(\displaystyle \,\)1,088,640

the answer in the back of the book is 30 240 tho...

xo_caroline_xo said:

the answer in the back of the book is 30 240 tho...

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Working from what you've learned in class and from the reasoning explained in the previous reply, what progress have made?

Thank you.

Eliz.

IF answer is 30240, then 1st 3 digits must be 1-3-6, 1-6-3, 3-1-6, 3-6-1, 6-1-3 and 6-3-1;
6 * 7! = 30240 : for each of those 6 "starts", you have 7! combos.

Smallest: 1-3-6-0-2-4-5-6-7-8-9
Highest: 6-3-1-9-8-7-6-5-4-2-0