Question

The number of ways in which four letters can be selected from the word degree?

Answer 1

To solve this question we must take cases Case 1 : all letters are distinct We have 4 distinct letters so 4C4 =1 Case2 : we have two distinct and two same So if we take two 3 than we must take 2 letter from other three letter 3C2=3 Case 3 : Three 3 letter same and one distinct So we have to select one letter from other three 3C1 =3 Total ways = 1+3+3. Hope you understand the answer....

Answer 2

Answer:

The Number of ways in which 4 letters can be selected is 7

Step-by-step explanation:

Given word: DEGREE

To find: No. of ways of selecting 4 letters.

Total letter in word " DEGREE" = 6

In which 3 are same .i.e., E

⇒ 4 different letters

Case I : When all are different letters.

             Then No of ways = $^{4}\textrm{C}_{4}$ = 1 ways.

Case II : When 3 alike 1 different Here it is to be noted that for 3 letters to be alike, only E is eligible since it is the only letter occurring 3 times. Then remaining single letter is to be selected from 3 types (D,G & R).

⇒ No. of ways =  $^{3}\textrm{C}_{1}$ = 3 ways.

Case III : 2 alike 2 different . Now 2 alike letters are again E.  Then remaining 2 letter is to be selected from 3 types (D,G & R).

⇒ No. of ways =  $^{3}\textrm{C}_{2}$ = 3 ways.

Hence, Total number of selection of 4 letters = 3 + 3 + 1 = 7 ways

Therefore, The Number of ways in which 4 letters can be selected is 7