Question

Please check the attachment for question

Answer 1

The expression $_nC_3$  is referring to the 4th number in the nth row of the Pascal triangle.

The expression $_nC_3$ is given.

We need to find which place number in the nth row of the pascal triangle the given expression represents.

What is a Pascal Triangle?

Pascal triangle is an arrangement of binomial coefficients in a triangular form and the middle numbers are filled such that each number is the sum of the two numbers just above it.

The elements of the nth row of Pascal's triangle are given by:

$^nC_0, ^nC_1,^nC_2,^nC_3,..........,^nC_n$

The formula for Pascal's triangle is:

$^nC_m = ^{n-1}C_{m-1}+^{n-1}C_m$

Where $^nC_m$ represents $(m+1)^{th}$ elements in the nth row.

We have,

$^nC_3~~or~~_nC_3$

So applying the Pascal triangle formula.

We see that we are referring to the 4th number in the nth row of the Pascal triangle.

Because $^nC_3$ represents $(3+1)^{th}$ element in the nth row of the pascal triangle.

$(3+1)^{th}~element = 4^{th}~element$

Learn more about the Pascal triangle here:

brainly.com/question/26134164

#SPJ1