find the digit in units place in the expansion of the following: 1) 2¹⁹⁶⁷ 2) 3¹⁹⁶⁹ 3)4¹⁹⁷⁰ 4) 4¹⁹⁷¹ 5) 5⁵⁵⁵ 6) 6¹⁰⁰⁰ 7) 7²⁰⁰⁷ 8) 8²⁰⁰⁹ 9) 9¹⁹⁹⁹ 10) 9²⁰⁰⁸. ​

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?