Question 1173343
.
<pre>

(a)  9 options for the most-left digit;

     8 remaining options for the next digit;

     7 remaining options for the next digit;

     6 options for the last digit.


     In all, there are  9*8*7*6 =  3024  such numbers.      <U>ANSWER</U>



(b)  " Less than 2000 "  means that the first digit is 1.


     Then there are 8 remaining options for the next digit;

                    7 remaining options for the next digit;

                    6 remaining options for the last digit.


     In all, there are  8*7*6 =  336  such numbers.       <U>ANSWER</U>




(c)  The last digit ("ones" digit) is any of four even digits 2, 4, 6 8, giving 4 options

     The "tens" digit is any of 8 remaining digits, giving 8 options;

     The "hundreds" digit is any of 7 remaining digits, giving 7 options;

     The "thousands" digit is any of 6 remaining digits, giving 6 options.


     In all, the number of options is  4*8*7*6 = 1344,  giving  1344 possible numbers.
</pre>

Solved - all questions are answered.


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If you want to see many similar solved problems on PERMUTATIONS, see my lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Permutations.lesson>Introduction to Permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-permutations.lesson>PROOF of the formula on the number of Permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Permutations.lesson>Simple and simplest problems on permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Special-type-permutations-problems.lesson>Special type permutations problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/How-many-different-permutations-may-exist-ubder-given-restrictions.lesson>Problems on Permutations with restrictions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/OVERVIEW-the-lessons-on-Permutations-and-Combinations.lesson>OVERVIEW of lessons on Permutations and Combinations</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Combinatorics: Combinations and permutations</U>". 



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.



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