Permutations online mains 2018 Q.1. The number of four letter words that can be formed using the letters of the word BARRACK is : a. 270 b. 264 c. 120 d. 144 Share with your friends Share 2 Neha Sethi answered this Dear student BARRACKThe given word is 'BARRACK'The number of letters=7B→1A→2R→2C→1K→1The number of different letters=5To make the 4 letters word following are the possible cases:1) 2 alike 2 alike2) 2 alike 2 different3) all the 4 letters are differentCase 1) 2 alike and 2 alike letters can be chosen out of three letters (i.e A,R(2C2×4!2! 2!=1×4×3×22×2=6 waysCase 2) 2alike and 2 different can be chosen alike letters out of 2 lettersand 2 different letters can be chosen out of remaining 4 different letters.Thus the number of words of such kind are2C1×4C2×4!2!=2×6×12=144 ways.Case 3) All the 4 letters are different.Out of 5 different letters the number of ways of choosing 4 letters=5C4=5 waysThus the number of words of such kind are=5×4!=120 ways.Thus the total number of 4 letters words which can be formed =6+144+120=270Note: nCr=n!r!n-r! Regards 0 View Full Answer
