perms and combs question (1 Viewer)

[daddywal]

Find the number of ways in which the letters of the word TRIANGLE can be arranged in a line:
i) so that all the vowels are next to each other
ii) so that consonants are in the two end positions?

 

[scaryshark09]

i) 8! / 3! = 6720
ii) no idea

 

[mmmmmmmmaaaaaaa]

ii) 5 * 4 * 6!
I) 6! * 3!
teamwork, howcanibesmarter

 

[howcanibesmarter]

in case u need explanations:

i) Since I, A, E must be together then we can consider them as one letter such that it can be presented like: [IAE] _ _ _ _ _. Now theres 6 letters to be arranged in a row, or 6! But the vowels can also appear in any order, so we need to rearrange the 3 vowels in a row too, so its 3! Therefore, answer = 6! * 3! = 4320

ii) If there are consonants at the two end positions, we want to deal with the restrictions first. For the 1st position, any of the letters T, R, N, G, L can be chosen. So theres 5 possible outcomes. For the last position, since one of T, R N, G, L is already used or the 1st position there is now 4 letters remaining. Any of remaining 6 numbers are then to be rearranged in a row, which gives 6!
Therefore, answer = 5* 4 * 6!

 

[scaryshark09]

in case u need explanations:

i) Since I, A, E must be together then we can consider them as one letter such that it can be presented like: [IAE] _ _ _ _ _. Now theres 6 letters to be arranged in a row, or 6! But the vowels can also appear in any order, so we need to rearrange the 3 vowels in a row too, so its 3! Therefore, answer = 6! * 3! = 4320

ii) If there are consonants at the two end positions, we want to deal with the restrictions first. For the 1st position, any of the letters T, R, N, G, L can be chosen. So theres 5 possible outcomes. For the last position, since one of T, R N, G, L is already used or the 1st position there is now 4 letters remaining. Any of remaining 6 numbers are then to be rearranged in a row, which gives 6!
Therefore, answer = 5* 4 * 6!

oh god, i tried learning perms and combs today, and looks like i failed...

 

[carrotsss]

oh god, i tried learning perms and combs today, and looks like i failed...

didn’t u accel ext 1 anyway

 

[scaryshark09]

didn’t u accel ext 1 anyway

no only adv