What is the sixth element in the tenth row of Pascal's triangle? For example, if we wanted to identify the sec

Question

What is the sixth element in the tenth row of Pascal's triangle? For example, if we wanted to identify the second element in the fourth row, it would be a 6. This is because we use the position number to find an element in a given row.
a. 56
b. 126
c. 210
d. 256

Answer 1

In row n, the k element is given by the formula:
C(n, k) = n! / k! (n-k)!

In your example, n = 10, k = 6
C(10, 6) = 10! / 6! 4!

= 10 x 9 x 8 x 7 / 4!
= 10 x 9 x 8 x 7 / 24
= 5 x 3 x 2 x 7
= 210

C(n,k) is known as the "binomial coefficient". You may also see it referred to in combinatorics as "n choose k".

Just to confirm the formula, C(4, 2) = 4! / 2! 2! = 24 / (2 x 2) = 6

Answer:
C) 210

Answer 2

yet another trick question ""The rows of Pascal's triangle (sequence A007318 in OEIS) are conventionally enumerated commencing with row n = 0 on the right (the 0th row). and comparable with the climate in each and each row, the 1st element is 0, no longer a million 10Row6Element = 10C6 (10 decide on 6) = 252 uncomplicated no tricks allowed interior the Triangle

Answer 3

That would be 10C5.
10C5 = 10*9*8*7*6/5! = 252.
So none of your choices is correct.
Remember the elements in a row are numbered
starting with 0,
So the element numbers are 0,1,2,3,4,5,6,7,8,9,10.
So the 6th element in row 10 is 10C5.
Google Pascal's triangle and you will see that
this is correct.

Answer 4

its 126

the 10th row is

1 9 36 84 126 126 84 36 9 1