Question

find the number of Combination of the letters of the word college taken 4 together a)18 b)16 c)20 d)26​

Answer 1

Answer:

Option (a) 18

Step-by-step explanation:

Given word

COLLEGE

Case (1) When all the letters are distinct

We choose 4 letters from 5 letters C, O, L, E, G

Total combinations $={5\choose 4}=5$

Case (2) When two letters are distinct and two letters are same

We choose 2 same letters from LL and EE in ${2\choose 1}$ ways and rest 3 letters from other 5 letters in ${5\choose 3}$ ways

Total ways $={2\choose 1}\times {4\choose 2}=12$

Case (3) When two letters are same and other two letters are same

The combination will be ${2\choose 2}=1$

Therefore, total combination of 4 letter words

$=5+12+1$

$=18$

Hope this answer is helpful.

Answer 2

Answer:

we should take 4 letters from the word college.

c, o, ll, ee, g.

case 1: we can take 4 distinct letters from 5 letters. so 5c4= 5

case 2: we can take one group( ll or ee) of two groups( ll, ee) and remaining three distinct letters from ( c, o, g, and ll or ee ( only one group)) so, 2c1 x 4c2 = 2 x 6 = 12

case 3: we can take two groups ie. four letters from two groups (ll, ee) itself. so 2c2 = 1

Now we are going to add three cases of choosing numbers. 5+12+1 =18