Answer to Question #299636 in Statistics and Probability for Nani

Question

Find the number of ways in which the word "BREAD' can be arranged when

i) B and D take end places

ii) E is placed in middle

iii) vowels E and A always come together

iv) vowels E and A never come together

Answer 1

i) B and D take end places

RAEBD

ERABD

EARBD

AERBD

AREBD

Thus it equals 6 ways

ii) E is placed in middle

BREAD, BREDA, BAEDR, BAERD, BDERA, BDEAR,RDEBA, RAEDB, RAEBD, RDEAB, AREBD, ABEDR,ABERD, AREDB,DBERA,ADERB,ADEBR,DBEAR,DREBA,DREAB, DEARB,DEABR, DAEBR,DAERB

Thus it equals 24 ways

iii) vowels E and A always come together

BREAD, BRDEA, BEARD, BEADR, BDREA, BDEAR, RBEAD, READB, REABD, RBDEA, RDBEA, RDEAB, EABRD, EABDR, EARBD, EADRB, EADBR, EARDB, DBREA, DREAB, DRBEA, DBEAR, DEABR,DEARB,

Thus it equals 24 ways

iv) vowels E and A never come together

this equals to (5*4*3*2*1) - ways that( vowels E and A always come together)

which yields ( 120)- (24) = 96 ways