A. How many ways can the letters of the word ALGORITHM be arranged in a row? b. How many ways can the letters of the word ALGORITHM be arranged in a row if A and L must remain together (in order) as a unit?
c. How many ways can the letters of the word ALGORITHM be arranged in a row if the letters GOR must remain together (in order) as a unit?

a). The number if ways it can be arranged in a row= 362880 ways

b). 40320 ways

c). 5040 ways

Step-by-step explanation:

There are 9 alphabets in the word ALGORITHM

The number if ways it can be arranged in a row= 9!

The number if ways it can be arranged in a row= 9*8*7*6*5*4*3*2*1

The number if ways it can be arranged in a row= 362880 ways

if A and L must remain together (in order) as a unit, then we take it as 8 alphabets

= 8!

= 8*7*6*5*4*3*2*1

= 40320 ways

if the letters GOR must remain together (in order) as a unit, then we have 7 alphabets units remaining

= 7!

= 7*6*5*4*3*2*1

= 5040 ways

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

answer: 1, 3 and 5 are correct

step-by-step explanation: