How many different strings can be formed by rearranging the letters in the word troposphere?

Step-by-step explanation:

The letters of the word troposphere can be sorted to be:

ee h oo pp rr s t

with 7 distinct letters of which 4 are in pairs for a total of 11 letters.

The number of words that can be formed from n distinct letters

= n!/(1!1!1!1!)   [n times in the denominator]

The number of words that can be formed from n letters of which 2 are duplicated and the rest distinct is

= n!/(2!1!1!1!)     [n-1 times 1!]

Similarly, the number of words that can be formed from 11 letters, of which there are 4 pairs of duplicated letters is

N=11! / (2!2!2!2!1!1!1!)

= 39916800 / (2*2*2*2*1*1*1)

= 2494800

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is