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15 problems match “combinations”. Clear

Non-decreasing rolls of a die ●●●○○ 50 ptsA fair die is tossed 6 times. What is the probability that on each toss, the number shown is greater than or equal to the number on the previous toss? Give your answer as a decimal rounded to four decimal places.
Ten ten-sided dice sum above 95 ●●●○○ 50 ptsTen fair dice are rolled together, each with equally likely faces numbered 1 through 10. Find the probability that the total of the ten top faces is greater than 95. Give your answer as a decimal.
Arranging letters of COMPUTE ●●●○○ 50 ptsHow many ways are there to arrange the letters of the word COMPUTE so that the vowels are in alphabetical order, or the consonants are in alphabetical order, or at least two vowels are next to each other?
Each player gets an ace ●●●○○ 50 ptsA standard 52-card deck is shuffled and 2 cards are dealt to each of 4 players. Find the probability that every player receives at least one ace. Give your answer as a decimal rounded to eight decimal places.
One ace per suit in pinochle ●●●○○ 50 ptsA player is dealt a 20-card hand from a double-deck pinochle deck of 80 cards, which contains 4 aces of each suit. Find the probability that the hand contains exactly 1 ace of each of the four suits. Round to four decimal places.