How to Find How Many 6 Digit Numbers Can Be Formed With the Given Digits :
Here we are going to see how to find how many 6 digit numbers can be formed with the given digits.
Question 1 :
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number.
(i) How many distinct 6-digit numbers are there?
(ii) How many of these 6-digit numbers are even?
(iii) How many of these 6-digit numbers are divisible by 4?
Solution :
In order to construct 6 digit number, let us write 6 dashes
____ ____ ____ ____ ____ ____
Number of ways to fill those 6 places = 6!/2! 2!
= (6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1)/(2 ⋅ 1)(2 ⋅ 1)
= 180 ways
Since the required number is even, we have two options to fill the unit places (2 or 4)
Case (i)
In case we use 2 in the unit place, we have 5 options (1, 1, 3, 3, 4)
number of ways = 5!/2!2! = 30
Case (ii)
In case we use 4 in the unit place, we have 5 options (1, 1, 3, 3, 2)
number of ways = 5!/2!2! = 30
Total number of ways in (i) and (ii) = 30 + 30 = 60 ways
In the last two places, we have to use 12, 32 or 24.
Case (i)
Using 12 in the last two places.
If we use 12 to fill the last two places, then we will have 4 options(1, 3, 3, 4) to fill up the 4 places.
Number of ways = (4!/2!) ⋅ 1 ⋅ 1
= 12
Case (ii)
Using 32 in the last two places.
If we use 32 to fill the last two places, then we will have 4 options(1, 1, 3, 4) to fill up the 4 places.
Number of ways = (4!/2!) ⋅ 1 ⋅ 1
= 12
Case (iii)
Using 24 in the last two places.
If we use 24 to fill the last two places, then we will have 4 options(1, 1, 3, 3) to fill up the 4 places.
Number of ways = (4!/2!2!) ⋅ 1 ⋅ 1
= 6
Hence the required number of ways = 12 + 12 + 6
= 30
After having gone through the stuff given above, we hope that the students would have understood "How to Find How Many 6 Digit Numbers Can Be Formed With the Given Digits".
Apart from the stuff given above, if you want to know more about "How to Find How Many 6 Digit Numbers Can Be Formed With the Given Digits".
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
May 22, 24 06:32 AM
May 17, 24 08:12 AM
May 14, 24 08:53 AM