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24 Feb 2012, 09:13
Kudos
Bookmarks
Hi
Could some please clarify the difference in counting approach for the below two examples i found on a maths website
example 1
how many 3 digit numbers can be formed from digits 2,3,4,5,7,9
answer explanation says - since all the 6 digits are available
3 digits can be formed in - 6 x 6 x 6 ways = 216
example 2
how many 3 letter words can we make from the letters in the word LOVE
answer explanation says - this is permutation and order is important so
3 letter words can be made in - 4 P 3 = 4! / (4 - 3)! = 24 ways
I am now confused - if I compare this to example 1 - why can't 3 letter words be made in - 4 x 4 x 4 ways = 64 ways
I would say order is important even in example 1 then ?
could some one please help to understand this.
Thank you in advance.
Could some please clarify the difference in counting approach for the below two examples i found on a maths website
example 1
how many 3 digit numbers can be formed from digits 2,3,4,5,7,9
answer explanation says - since all the 6 digits are available
3 digits can be formed in - 6 x 6 x 6 ways = 216
example 2
how many 3 letter words can we make from the letters in the word LOVE
answer explanation says - this is permutation and order is important so
3 letter words can be made in - 4 P 3 = 4! / (4 - 3)! = 24 ways
I am now confused - if I compare this to example 1 - why can't 3 letter words be made in - 4 x 4 x 4 ways = 64 ways
I would say order is important even in example 1 then ?
could some one please help to understand this.
Thank you in advance.
25 Feb 2012, 09:19
Kudos
Bookmarks
The difference between EX1 and EX2 is that EX1 you can reuse digits. In EX2 cannot reuse digits so thats why its not 4 * 4 *4. Instead you can view it this way and do not have use Permutations.
Ex2 4 * 3 *2 = 24 The Reason you decrease each consecutive number is because one number gets used in a slot. So in the first slot you have 4 numbers to choose from. In the second slot you have 3 numbers to chose from and in third slot you have 2 numbers to choose from. Then multiplying them together you get the same result as the Permutation formula.
Hope this helps.
Ex2 4 * 3 *2 = 24 The Reason you decrease each consecutive number is because one number gets used in a slot. So in the first slot you have 4 numbers to choose from. In the second slot you have 3 numbers to chose from and in third slot you have 2 numbers to choose from. Then multiplying them together you get the same result as the Permutation formula.
Hope this helps.
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