pls help! (1 Viewer)

[allybee]

im having some trouble with these questions. They’re under the topic of Binomial theorem, combinations and permitations. Any help would be great

1)Find the value of n if <SUP>n+1 </SUP>P<SUB>2 </SUB>= 4n +10

2)how many parallelograms are formed by a set of 4 parallel lines intersecting another set of 7 parallel lines?

 

[jyu]

im having some trouble with these questions. They’re under the topic of Binomial theorem, combinations and permitations. Any help would be great

1)Find the value of n if <SUP>n+1 </SUP>P<SUB>2 </SUB>= 4n +10

2)how many parallelograms are formed by a set of 4 parallel lines intersecting another set of 7 parallel lines?

(1) <SUP>n+1 </SUP>P<SUB>2 </SUB>= 4n +10,
(n + 1)n = 4n + 10,
n^2 + n = 4n + 10,
n^2 - 3n - 10 = 0,
(n - 5)(n + 2) = 0, .: n = 5

(2) (0 + 1 + 2 + 3)(0 + 1 + 2 + 3 + 4 + 5 + 6) = 6 x 21 = 126

 

[allybee]

it finally makes sense now
thanks