### Quiz Question 16: Given 5 double digits a,b,c,d,e that are both different and different from 0. The set of 5 digit natural numbers including 5 digits a,b,c,d,e (in where the digit a is always in the tens of thousands position) how many elements are there.

Think and answer the question before looking at the answer

List the elements of the set.

There are 6 numbers where the digit a is always in the tens of thousands place and there is a digit b in the thousands place:

\(\overline {abcde} ,\overline {abced} ,\overline {abdce} ,\overline {abdec} ,\overline {abecd} ,\overline {abedc}\)

Because the roles of b, c, d, e are the same, when we put c, d, e as the thousands digit, we get the same results.

So the resulting numbers are 6.4 = 24 numbers.

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QUIZ MATH 6