There is a 70 percent chance that an airline passenger will check bags. next, consider 16 passengers that check in for their flight at denver international airport. what is the probability that all of them will check bags?

Binomial distribution because all following requirements are fulfilled.
1. Bernoulli trials, i.e. exactly two possible outcomes (check or not check)2. Number of trials is known before and constant throughout the experiment, i.e. independent of outcomes. (16 passengers)3. All trials are independent of each other (assumed from context)4. Probability of success is known, and remain constant throughout trials (70%)Since all criteria are satisfied, we can model with binomial distribution, where the probability of x successes out of N trials each with probability of success p is given byP(x)=C(N,x)(p^x)(1-p)^(N-x)and,C(N,x) is number of combinations of selecting x objects out of N.
P(16)=C(16,16)*(0.7^16)(1-0.7)^0
=1*0.003323*1
=0.003323

The answer would be 27 because assuming that each package has 1 bar of soap and 1 tube of toothpaste, after 27 packages they would run out of toothpaste