Homework SourseA bag contains 2 red marbles 4 green ones 1 lavender one 6 y
A bag contains 2 red marbles, 4 green ones, 1 lavender one, 6 yellows, and 2 orange marbles. HINT [See Example 7.] How many sets of four marbles include all the red ones?
A bag contains 5 red marbles, 3 green ones, 1 lavender one, 1 yellow, and 2 orange marbles. HINT [See Example 7.] How many sets of four marbles include none of the red ones?
A bag contains 2 red marbles, 3 green ones, 1 lavender one, 6 yellows, and 4 orange marbles. HINT [See Example 7.] How many sets of four marbles include one of each color other than lavender?
A bag contains 3 red marbles, 2 green ones, 1 lavender one, 1 yellow, and 3 orange marbles. HINT [See Example 7.] How many sets of five marbles include at least two red ones?
A bag contains 4 red marbles, 1 green one, 1 lavender one, 3 yellows, and 3 orange marbles. HINT [See Example 7.] How many sets of five marbles include at most one of the yellow ones?
If a die is rolled 25 times, there are 625 different sequences possible. The following question asks how many of these sequences satisfy certain conditions. HINT What fraction of these sequences have exactly five 1s? (Round your answer to four decimal places.)
Solution
1. There are 2 red marbles and 13 others.
So the question is, how many combinations of the 13 others are possible, taking 2 at a time?= 13C2
13*12/2 = 78, that\'s the answer
2. There are 5 red marbles and 7 others.
So the question is, how many combinations of the 7 others are possible, taking 4 at a time?= 7C4
7*6*5/6 = 35, that\'s the answer
3.we have to select 1 from each colour. 2C1*3C1*6C1*4C1=144 that\'s the answer.
4.it is sum of cases when we have 2 red marble plus when we have 3 red marble
case of 2 red marble= 7C3=35
case of 3 red marble= 7C2=21
total= 35+21=56
5. it is case of 0 yellow plus 1 yellow
0 yellow- 9C5=126
1 yellow- 9C4=126
total= 126+126=252
6. There are 25C5 = 53130 combinations of particular rolls which could come up as the five 1s.
For each of these, the other 20 rolls can each be any of the other five numbers, so the answer is
25C5 * 5^20 / 6^25
= 0.1782
![A bag contains 2 red marbles, 4 green ones, 1 lavender one, 6 yellows, and 2 orange marbles. HINT [See Example 7.] How many sets of four marbles include all the](/WebImages/39/a-bag-contains-2-red-marbles-4-green-ones-1-lavender-one-6-y-1120938-1761596516-0.webp "A bag contains 2 red marbles, 4 green ones, 1 lavender one, 6 yellows, and 2 orange marbles. HINT [See Example 7.] How many sets of four marbles include all the")
