Find the number of 4-letters words possible by taking 4 letters from the word "INKLING".
Case 1: No repeated letters from these 5: {I,N,K,L,G}
Choose the 1st letter 5 ways.
Choose the 2nd letter 4 ways.
Choose the 3rd letter 3 ways.
Choose the 4th letter 2 ways.
That's 5P4 = 5*4*3*2 = 120 ways for case 1.
Case 2: There are 2 I's but not 2 N's
Choose the 2 positions for the I's 4C2 = 6 ways
Choose the letter for the leftmost unchosen position 4 ways, from {N,K,L,G}
Choose the letter for the rightmost unchosen letter 3 ways.
That's 6*4*3 = 72 ways for case 2.
Case 3: There are 2 N's but not 2 I's
Same as Case 2.
That's also 72 ways for case 3.
Case 4. 2 N's and 2 I's
Choose the positions for the N's 4C2 = 6 ways.
Put I's in the remaining 2 places only 1 way.
That's 6*1 = 6 ways for case 4
Grand total: 120+72+72+6 = 270
Answer: Choice (A)270
Edwin
