In the game of JUMBLE, the letters of a word are scrambled. The player must form the correct word. In a recent game in a local newspaper, the Jumble “word” was LINCEY. How many different possible arrangements of these letters are there to form different 6 letter words?
+118687 Isilber17 is correct I shall try to explain.
There are 6 letters and they are all different.
I will assume that the letters cannot be repeated - I think that is the intended meaning of the question.
You choose the fist letter there are 6 possible outcomes.
now you choose the next letter, there are 5 possible ourcomes because one has already been chosen.
so the number of ways 2 letters can be chosen is 6*5
now you choose the third letter. there are 4 possible letters available to choose from.
So the number of ways you can choose 3 letters is 6*5*4
etc
the number of ways you can choose all 6 letters where the order is very important is 6*5*4*3*2*1 = 6!
Does that help?
+109 with repitition $${{\mathtt{6}}}^{{\mathtt{6}}} = {\mathtt{46\,656}}$$
without repitition $${\mathtt{6}}{!} = {\mathtt{720}}$$
I don't know how many combinations would specifically form an existing word.
+118687 Isilber17 is correct I shall try to explain.
There are 6 letters and they are all different.
I will assume that the letters cannot be repeated - I think that is the intended meaning of the question.
You choose the fist letter there are 6 possible outcomes.
now you choose the next letter, there are 5 possible ourcomes because one has already been chosen.
so the number of ways 2 letters can be chosen is 6*5
now you choose the third letter. there are 4 possible letters available to choose from.
So the number of ways you can choose 3 letters is 6*5*4
etc
the number of ways you can choose all 6 letters where the order is very important is 6*5*4*3*2*1 = 6!
Does that help?
