Bibi's Malfunctioning Phone

As we have to select 3 person, out of which 2 are from 21 person (who were supposed to be invited), and 1 is from 16 (who were not supposed to be invited) to ensure that exactly one person who got the invitation was not supposed to be invited to the party. So favorable event =(21C2)*(16). Also total possible 3 selection are (37C3). Thus we get ans=16/37 or a+b=53

She does not want to invite 16 of the 37 people. So, exactly one from them is 16C1. The remaining are selected from 21 i.e. 21C2. So, the answer is: (16C1*21C2)/(37C3) = 16/37. Hence, a=16, b=37 => a+b = 53.

total list of friends=37, selected friends 21, unselcted friends =16 so we are interested in group of 3 friends such that 1 is from the list of unselected and 2 from the other list hence total no of such groups=(16 C 1) X (21 C 2) total nos of groups of 3 friends from total list of 37=(37 C 3) so from definition, the probability that exactly one person who got the invitation was not supposed to be invited= (16 C 1) X (21 C 2) / (37 C 3) =16/37

so the answer is 16+37=53

total contacts = 37 , friends to be invited = 21, left over contacts = 37 -21 = 16 all 16 having the probability to receive the invitation out of total contacts. Hence the probability is 16/37, which gives $a= 16, b= 37, a + b = 16 + 37 = 53$ .

There are $\binom{37}{3}$ possible sets of three people that the message could have gone to. The number of ways the message could go to 2 invited people and one uninvited person is $\binom{21}{2}\binom{18}{1}$ . Thus, the probability that exactly one person got the invitation that shouldn't have is: $\frac{\binom{21}{2}\binom{16}{1}}{\binom{37}{3}} = \frac { \frac {21 \times 20} {2} \times 16} { \frac {37 \times 36 \times 35} {3 \times 2} } = \frac{16}{37}$ Therefore $a + b = 16 + 37 = 53$ .

The probability of the phone selecting one person from the three is 1. The probability of the phone selecting exactly one friend who was not supposed to be invited is $\frac {21}{37}$ . Therefore the probability of the phone selecting a person that was not intended to attend the party is as follows: 1- $\frac {21}{37}$ = $\frac {16}{37}$

The total of a + b is therefore 16 + 37 = 53 .