Luke has a set of cards numbered 1 to 8, which he arranges in pairs. He notes the sum of the numbers on each pair of cards and calculates
the lowest common multiple (LCM) of the four sums.

Luke now takes six cards numbered I to 6 but he groups them into
two sets of three. He finds the sums of the numbers in each triple and
then finds the LCM of these two triple sums. What is the smallest
LCM he can obtain?​

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?