Question

The number of different combinations that can be formed out of the letters of the word 'INFINITE' taken four at a time is

• A. $20$
• B. $22$
• C. $24$
• D. $120$

Answer 1

The correct option is B $22$

Total letter $=3I+2N+F+T+E=8$

Case 1: When 3 same + 1 different $=1{\times }^4{C}_1$
Case 2: When 2 same + 2 same $=1\times 1=1$
Case 3: When 2 same + 2 different $=1{\times }^4{C}_2+1{\times }^4{C}_2$
Case 4: When all are different ${=}^5{C}_4$
Therefore total ${=}^4{C}_1+1+{}^4{C}_2+{}^4{C}_2+{}^5{C}_4=22$