To compute how many groups of elements we can extract out of a group of elements, we can use the binomial coefficient:
where the factorial is defined as
So, this is the number of possible quintuplet out of 50 numbers:
Similarly, this is the number of possible groups of six numbers out of 60:
So, you win with a combination out of 2118760 in state A, and with a combination every 50063860 in state B this means that winning in state A is easier with a ratio of
Whichi means that winning in state B is 23 times harder
Answer:
7.7 square metres or 7.669 square metres of metal sheet
Step-by-step explanation:
Volume of cylinder = 2×22/7×r×100cm
15.4 litres = 15,400 cm cube
Radius = 15 400×7/22 × 50
= 98cm
Surface area of cylinder = (2×22/7×49^2) + (2×22/7×49 × 100)
= 15 092 + 61 600
= 76 692 square cm
= 7.669 square metres of metal sheet required
Answer:
Step-by-step explanation:
Let x represent the distance travelled by the helicopter and the plane.
Let t represent the time it takes the the helicopter to travel x miles
Speed of the helicopter is 180 miles per hour.
Distance travelled = speed × time
x = 180t
Twenty minutes later, a plane leaves the airport and follows the helicopter at 330mi/hr. Converting 20 minutes to hours, it becomes 20/60 minutes
Time taken for the plane to travel x miles is t - 20/60
x = 330(t - 20/60)
Before the plane overtakes the helicopter, they would have travelled equal distance. Therefore
330(t - 20/60) = 180t
330t - 110 = 180t
330t - 180t = 110
150t = 110
t = 110/150 = 0.73 hours