Question

How many four letter words can be formed using the letters of the word FAILURE, so that F is included in each word?

• A. 400
• B. 420
• C. 460
• D. 480

Answer 1

Answer: (D)

There are 7 letters in the word FAILURE. To include F in every 4 letters word, we first select four letters from the 7 letters of the word FAILURE such that F is included in every selection. This can be done by selecting three letters from the remaining six letters. ie, $A,I,L,U,R,E$ in ${}^6{C}_3$ ways. Now there are 4 letters in each of ${}^6{C}_3$ selections. Also every selection contains letters which can be arranged in 4! ways. Hence, the required number of four letter words ${=}^6{C}_3\times 4!=\frac{\mathrm{6.5.4}}{\mathrm{3.2.1}}.24$ $=20\times 24=480$