# we wish to select 6 persons of 8,but if the person A is selected then B must be chosen. in how many ways can the selection be made?(plz explain)

148 Points
14 years ago

Dear ajinkya

case 1  :   A and B is not included

then number of ways = 6C6 = 1

case 2 : B is selected A is not selected

number of ways  = 1* 6C5  = 6

case 3:  A and B both are selected

number of ways = 1*1* 6C4 = 15

so total ways  = 1+6+15 =22

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13 Points
6 years ago
i) When A is chosen: In this case we can chose the remaing 5 from 7 in 7C5 ways
​ii) When A is not chosen: In this case B is not chosen as well. So we now have to select all 6 from the remaining 6 (as A and B have been removed from the previous 8). This can be done in 6P6 ways.
Hence, the required number of ways = 7C6P6  = 7!/ 5! x 2! + 6!/ 6! x 0! = 7x6/2 + 6!/6! = 21+1 = 22
Dinabandhu
13 Points
5 years ago
Sir I think in second method there is a typo. It should be C(6, 6)  and not P(6, 6)  as given.
Because P(6, 6) =6! And not 1 as given.
Question is very old and it does not matter but at age of 50 I am trying to learn maths again and I salute your effort
Rishi Sharma
3 years ago
Dear Student,

case 1 : A and B is not included
then number of ways = 6C6 = 1
case 2 : B is selected A is not selected
number of ways = 1* 6C5 = 6
case 3: A and B both are selected
number of ways = 1*1* 6C4 = 15
so total ways = 1+6+15 =22

Thanks and Regards