Connections Academy
what is 3! simplified as
a 2
b 5
c 3
d 6***
simplify 10p4
a 210
b 360
c 5,040***
d 151,200
simplify 15c3
a 182
b 455***
c 2,730
d 910
my answers
1-d
2-c
3-b
All three are correct.
Thanks I got 100%
tank yu
To simplify the expressions, we need to understand some mathematical concepts.
1) 3!
The exclamation mark in mathematics represents the factorial of a number. The factorial of a positive integer n, denoted by n!, is the product of all positive integers from 1 to n.
For example, 3! = 3 x 2 x 1 = 6.
In the given options, we are asked to find the simplified value of 3!. Looking at the options, option d (6) is the correct simplified value.
Therefore, the correct answer for 3! simplified is d) 6.
2) 10P4
The notation 10P4 represents the permutation formula. Permutations are the ordered arrangement of objects or items without repetition.
The formula for permutations is given by nPr = n! / (n - r)!
For example, 10P4 = 10!/ (10-4)! = 10!/6! = (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (6 x 5 x 4 x 3 x 2 x 1) = 210.
Looking at the options, option c (5,040) is the incorrect answer, as it is not the simplified value of 10P4.
Therefore, the correct answer for 10P4 simplified is a) 210.
3) 15C3
The notation 15C3 represents the combination formula. Combinations are the selection of objects or items without regard to the order.
The formula for combinations is given by nCr = n! / (r! (n - r)!)
For example, 15C3 = 15! / (3! (15-3)!) = 15! / (3! 12!) = (15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1) (12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = 455.
Looking at the options, option b (455) is the correct simplified value for 15C3.
Therefore, the correct answer for 15C3 simplified is b) 455.
Based on the explanations provided, your answers are incorrect.
Correct answers:
1) d) 6
2) a) 210
3) b) 455