Answer:
1. 5040
2. 20
Step-by-step explanation:
1. using the formula for permutation
nPr=n!/(n-r)!
10P4 = 10!/(10-4)!
=10*9*8*7*6!/6!
then we are left with
=10*9*8*7
=5040
2.using the formula for combination
nCr=n!/(n-r)!r!
6C3=6!/(6-3)!3!
=6*5*4*3!/3!3!
=6*5*4/3*2*1
=20
This is a simple problem based on combinatorics which can be easily tackled by using inclusion-exclusion principle.
We are asked to find number of positive integers less than 1,000,000 that are not divisible by 6 or 4.
let n be the number of positive integers.
∴ 1≤n≤999,999
Let c₁ be the set of numbers divisible by 6 and c₂ be the set of numbers divisible by 4.
Let N(c₁) be the number of elements in set c₁ and N(c₂) be the number of elements in set c₂.
∴N(c₁) =

N(c₂) =

∴N(c₁c₂) =

∴ Number of positive integers that are not divisible by 4 or 6,
N(c₁`c₂`) = 999,999 - (166666+250000) + 41667 = 625000
Therefore, 625000 integers are not divisible by 6 or 4
Answer:
<h3>The ratio of technicians to all helpers is 11 : 7, or

or 11 to 7.</h3>
Step-by-step explanation:
- Given that there are 7 ushers and 11 technicians helping at the Harper Middle School fall play.
- Let x be the number of ushers ( or helpers ).
- Therefore x=7 helpers.
- Let y be the number of technicians.
- Therefore y=11 technicians.
<h3>To find the ratio of technicians to all helpers :</h3>
That is to find the ratio of y to x.
We can write the ratio of technicians to all ushers(helpers) as y : x
Which implies that 11 : 7, (since y=11 and x=7)
Or
or 11 to 7
<h3>The ratio of technicians to all helpers is 11 : 7, or

or 11 to 7</h3>
HOPE THIIIISSS HELLLPSSSS
First lets figure out what -5+5 equals. so -5+5=0. so then -4-0 equals -4. so therefor your answer is -4