Dragons have to meet for a brainstorm in a convention center. The delegates have to be selected to provide the maximum efficiency of the brainstorm session. A dragon has any amount of heads, and for any N, any amount of N-headed dragons is available if needed. The problem is that the size of the convention center is limited so no more than 1000 heads can fit into the assembly hall. The intellectual power of a dragon pack is the product of head numbers of dragons in the pack. How should an optimum pack look like (the total number of dragons, the head number distribution)?
Weights of the 5 boxes are positive integers and their mean as well as median is 6. If the only mod is 8, then find the sum of weights of heaviest box and lightest box.
chance of any two of them being born on same day is =1- chance of all of them being born on different days.total number of possible ways = 7^7now first person can be born on any of the 7 days, next person can be born on any of the 6 days, next person can be born on any of remaining 5 days....and so on.So possible no. of ways in which all are born on different days = 7*6*5..*2*1 = 7!hence chance that at least 2 of them are born on same day = 1- 7!/7^7 = 1 - 6!/7^6 ATDH.
Can you check my method?
Out of 7 persons i selected 2 persons in 7C2 ways
Out of 7 days i selected 1 day in 7C1
Total ways 7^7
chance =7C2*7C1/7^7
In a room there are 7 persons. The chance that 2 of them were born on the same day of the week is?
On the surface of the planet lives a vampire , that can move with the speed not greater than u. A vampire slayer spaceship approaches to the planet with its speed v. As soon as the spaceship sees the vampire it shots a silver bullet - the vampire is dead. Prove that if v/u > 10 , the vampire slayer can accomplish his mission, even the vampire is trying to hide.
Let X be a four-digit positive integer such that the unit digit of X is prime and the product of all digits of X is also prime. How many such integers are possible?
Let X be a four-digit positive integer such that the unit digit of X is prime and the product of all digits of X is also prime. How many such integers are possible?
Let X be a four-digit positive integer such that the unit digit of X is prime and the product of all digits of X is also prime. How many such integers are possible?
Product is prime. so three numbers will be 1, 1, 1
