**Hi..i have a doubt in permutation and combination..

i already know permutation is an a method of arrangement of a set of n objects in a given order that means in permutation order of objects is important .

combination is a method of total ways of doing a particular task ..here order of objects in the selection does not matter.

But if a question is given as follows how to identify whether this question is of permutation or combination.

How many integers between 100 and 999 consist of distinct even digits.

I have done as follows The total no of even digits are(0,2,4,6,8)=5 and a number is identified as even by its last digit.

As first digit can not be 0 so it can take any of the 9 digits(1-10) Second digit can take 8 3rd digit can take 5 so my answer came out to be 9*8*5.

is it correct**


First of all if question is specifying "distinct even digits", it means you can use only digits out of the set $\{0,2,4,6,8\}$.

Moving forward, To identify if the question is of permutation or combination is simple. What you said is right, if the order of objects of selection matters, it's permutation else it's combination. For example here, if you select the first integer out of $\{0,2,4,6,8\}$, you are not allowed to select it again.

Thus, the total number of such numbers is $4\times4\times3 = 48$.

  • $\begingroup$ but in my book ans is given as 4*5*5 $\endgroup$ – Shivangi Bhatnagar Dec 8 '14 at 14:29
  • $\begingroup$ Yes, because the question is NOT asking about even numbers, it asks you for numbers with even digits $\endgroup$ – Abhinandan Dubey Dec 8 '14 at 14:31
  • $\begingroup$ but in my book ans is given as 4*5*5 $\endgroup$ – Shivangi Bhatnagar Dec 8 '14 at 14:33
  • $\begingroup$ It's probably wrong then. Because For first (hundredth's place you can have 4 possibilities, then for tens place you are left with 4 again (because you can use zero here), the ones place is left with only 3 integers. Thus the number = 4*4*3=48 $\endgroup$ – Abhinandan Dubey Dec 8 '14 at 14:38
  • 1
    $\begingroup$ 4*5*5 would be the answer if the digits did not need to be distinct. $\endgroup$ – epimorphic Dec 8 '14 at 14:38

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