Permutations (1 Viewer)

[philly2000]

Hi i need some guidance with these questions.

1. How many numbers greater than 4000 can be formed from the figures 3, 5, 7, 8, 9? (Repetitions are not allowed).

2. If 6Pr = 120 find the value of r.
6!/(6-r)! = 120 ; is there a way to expand the (6-r)! ?

3. Show that nPr = (n-2)Pr + 2r x (n-2)P(r-1) + r(r-1) x (n-2)P(r-2).

4. Find the number of arrangements of the letters in the word pencils if e precedes i.

thanks!

 

[addikaye03]

Hi i need some guidance with these questions.

1. How many numbers greater than 4000 can be formed from the figures 3, 5, 7, 8, 9? (Repetitions are not allowed).

2. If 6Pr = 120 find the value of r.
6!/(6-r)! = 120 ; is there a way to expand the (6-r)! ?

3. Show that nPr = (n-2)Pr + 2r x (n-2)P(r-1) + r(r-1) x (n-2)P(r-2).

4. Find the number of arrangements of the letters in the word pencils if e precedes i.

thanks!

_ _ _ _ ( four numbers) or _ _ _ _ _ now for the number to be >4000 it need to 4 or 5 digits long so

4 digits: first can only be 7 8 or 9, second can be any of the 5 but since the first space is occupied by a number there is only 4 then 3 then 2

so its 3x4x3x2

5 digits: Any 5 for the first, then so on so its 5x4x3x2x1

4x4x3x2 + 5!

96+ 120= 216 ways

2. 6Cr=120 therefore 6!/(6-r)!=120.... see how you go from there

4. Since its equally like that i proceeds e as e proceeds i, therefore its /2... since theres no repetitions its just 7!/2

I'll do three if no one else does later

 

[philly2000]

Oh ok thanks
but for the first question i think you made a mistake,
the 4 digits, the first can be 5 7 8 or 9
so its 4x4x3x2 = 96
96+120 = 216

and for question 2, Whered the combination come from? It was 6Pr = 120.
i got 6!/(6-r)! = 120
6! = 120(6-r)!
6!/120 = (6-r)!
6 = (6-r)!
i know r = 3 but how should i write it?

 

[lychnobity]

Oh ok thanks
but for the first question i think you made a mistake,
the 4 digits, the first can be 5 7 8 or 9
so its 4x4x3x2 = 96
96+120 = 216

and for question 2, Whered the combination come from? It was 6Pr = 120.
i got 6!/(6-r)! = 120
6! = 120(6-r)!
6!/120 = (6-r)!
6 = (6-r)!
i know r = 3 but how should i write it?

Write 3! = 6, therefore 6-r = 3

 

[philly2000]

Write 3! = 6, therefore 6-r = 3

Ah ok thanks!