(a)The possibilities are,Originally Posted byhotmail590

AXBXX This is (1)(3)(1)(2)(1)=6

BXAXX This is (1)(3)(1)(2)(1)=6

XAXBX ................................

XBXAX

XXAXB

XXBXA

Total=6 (times total arragement =6)=36

The number of ways to arrange 5 people is

(5)(4)(3)(2)(1)=120

Thus, probability is 36/120=3/10

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(b)

The possibilities are,

AXXBX This is (1)(3)(2)(1)(1)=6

BXXAX This is (1)(3)(2)(1)(1)=6

XAXXB ....................................

XBXXA

Total=6(times total arragement=4)=24

The number of ways to arrange 5 people is

(5)(4)(3)(2)(1)=120

Thus, the probability is 24/120=1/5=2/10

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(c)This only happens when,

AXXXB =6

BXXXA =6

In total we have 12, thus the probability is,

12/120=1/10

Thus the answers respectively are,

30% , 20% , 10%