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# Permutation and combination MATH

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Identify if given problem a permutation or a combination (^o^)✨ and solving too pls ty

6. A combo meal consists of three choices for rice, 4 choices for viand and 2 choices for drinks is being offered. How many ways can a'meal be prepared with one choice from each menu?

7. In a PTA meeting, there were 12 officers elected consist of four fathers and eight mothers. How many ways can they be arranged in a row for pictorial such that all fathers are to be side by side?
8. How many ways can one arrange the word ILOILO such that it starts and ends in 0.

9. There are eight black, four blue and 3 red pens inside the box. If 3 pens were randomly chosen, how many ways can this be done such that there is one pen for each color?

10. Four books from each year level of Math and English are to be arranged on a shelf such that they are arranged alternately. How many of this kind of arrangement can be done?​

Mar 1, 2022

#1
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Here's some

6)  This isn't a perm or a comb prob....it's just a counting prob

The number of possible meals =  3 * 4 * 2   =  24 possible meals

7)  The fathers grouped together can occupy 9 diiferent positions  and  for each of these they can be arranged in 4! ways.....and for each of these the mothers can be arranged in 8!  ways

Again.....this is really nothing more than  a counting problem.....the number of ways are

9 * 4! * 8!  =    8709120  ways

8)  Note that, since the O's are identical, there is only  1  identifiable way that they start and end a "word"

And  the other 4 letters  can be arranged  in        4!  / (2! * 2!) =  6 identifiable ways

So  1  *  6 =    6 identifiable ways   Mar 1, 2022
#2
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9)   Again, we just have a counting problem which can be expressed  as a combo multiplication

Choose  1  of each color and we  have

8C1  *  4C1  *  3C1   =

8    *    4     *  3   =

96   ways

10 )     Obviously  an English book could come first or  a Math book could come first  = 2 ways

And for  each of these.....we can permute each type of book in 4!  ways

So     2 C1  *  4!  * 4!    =   2 * 24 * 24   =    1152  ways   Mar 1, 2022