Submitted by robert.marik on Thu, 11/08/2018 - 12:47
Question:
Without calculator, simplify and evaluate the following expressions (for $n\in\mathbb N$). For each expression choose its correct value and if it isn’t in the table, choose X.
Suppose the coefficient of the quadratic term (i.e. the coefficient at \( x^2 \)) in the expansion of \( (1+x)^n \) equals \( 300 \). Find the value of the exponent \( n \).
On a lock of a safe deposit box a ten-digit code can be set. The code can consist only of four \( 1 \)s, three \( 2 \)s, two \( 3 \)s, and one \( 4 \). How many ways are there to set the code?