Year 11 Perms and Combs help (maths ext 1) (1 Viewer)

[hs17]

14 a How many seven-letter words can be formed without repetition from the letters of the word INCLUDE?

b How many of these do not begin with I?

c How many end in L?

d How many have the vowels and consonants alternating?

e How many have the C immediately following the D?

f How many have the letters N and D separated by exactly two letters?

g How many have the letters N and D separated by more than two letters?



Note: I only need help with f and g

 

[TheShy]

F) So one way of having them would be N_ _ D _ _ _. where the _ are the other letters. You can have this pattern a total 4 times ( N_ _ D _ _ _ , _ N _ _ D _ _, _ _ N _ _ D _, _ _ _ N _ _ D) Then, N and D can be aranged 2! times, ND and DN. Also, the other letters can be arranged 5!. Thus the answer should be 4*2!*5! = 960. I may be incorrect so check with the answers

 

[TheShy]

G) You should be able to solve part g, by using the same thing as part one. In this you have to find when N and D are seperated by more than two letters. You know how many can be formed when they are seperated by exactly two. Use the same way of answering part F) to find how many words form when ND and seperated by one letter and how many words are formed when they are together (seperated by no words). Then add them all up and 7! (thats how many words can be formed from INCLUDE) - whatever you get when you add them all up. This should be the answer, but once again, I am not 110% sure, check with the answers to make sure.

 

[hs17]

Yes that's correct, thanks!

 

[cocolo340]

Is this from the Cambridge textbook cause i was just doing that question as well

 

[hs17]

Yep..chapter 14c i'm pretty sure