henrymba2021 wrote:

In how many different ways can the letters A, A, B, B, B, C, D, E be arranged if the letter C must be to the right of the letter D?

a. 1,680

b. 2,160

c. 2,520

d. 3,240

e. 3,360

These are the arrangements possible where letter C is to the right of D

D******C

D*****C*

D****C**

D***C***

D**C****

D*C*****

DC******(7 combinations when D is the first alphabet)

*D*****C

*D****C*

*D***C**

*D**C***

*D*C****

*DC*****(6 combinations when D is the second alphabet)

**D****C

**D***C*

**D**C**

**D*C***

**DC****(5 combinations when D is the third alphabet)

The total arrangements possible are \(7+6+5+4+3+2+1 = 28\)

The total ways in which alphabets A,A,B,B,B,C can be arranged are\(\frac{6!}{2!*3!} = \frac{6*5*4*3*2}{2*3*2} = 6*5*2 = 60\)

Therefore, the total ways in which the alphabets can be arranged when C is to the right of D is 28*60 =

1680(Option A)
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