crejoc wrote:How many words (arrangements of letters) containing 3 consonants and 2 vowels can be formed from the letters of the word promise?
kindly explain..
First, we need to choose our letters.
For consonants, we want to select 3 out of 4. For vowels, we want to select 2 out of 3.
We don't care about the order in which we select them, so we use the combinations formula. We're selecting 3 consonants AND 2 vowels, so we MULTIPLY the results:
4C3 * 3C2 = 4!/3!1! * 3!/2!1! = 4*3 = 12
Once we select our letters, we need to arrange them into different configurations. We have 5 letters to arrange with no duplicates (the answer would be different if we had two "E"s on our list, for example). Since we're arranging we care about order, so we use the permutations formula:
5P5 = 5!/0! = 5! = 5*4*3*2 = 120
So, we have 12 different selections of letters and 120 ways to arrange our letters once selected. We're doing multiple steps, so we MULTIPLY the results:
12*120 = 1440.
Some important formulas:
nCk = n!/k!(n-k)!
nPk = n!/(n-k)!
in both formulas, n=total # of objects and k=# of objects used.
For permutations, if n=k (i.e. you're using all the objects), the total number of arrangements is simply n!.
Some good combinations shortcuts to remember:
nCn = 1
nC0 = 1
nC1 = n
