Final answer:
To find the probability that every student gets at least one cookie when 10 cookies are distributed among 5 distinct children, we can use the concept of stars and bars. The probability is approximately 51.48%.
Step-by-step explanation:
To find the probability that every student gets at least one cookie, we need to consider the number of ways the To find the probability that every student gets at least one cookie, we need to consider the number of ways the cookies can be distributed among the children. There are 10 cookies and 5 children, so we can think of this problem as distributing 10 identical items into 5 distinct groups.
This can be solved using the concept of stars and bars. We can represent the distribution as a sequence of stars (representing the cookies) and bars (representing the divisions between the children). We have 10 stars and 4 bars, as there are 4 divisions between 5 children. The number of ways to arrange the stars and bars is then given by the formula (10+4) choose 4.
Therefore, the probability that every student gets at least one cookie is ((10+4) choose 4)/10^5 which simplifies to (14 choose 4)/10^5.
Using the formula for combinations, (n choose r) = n!/(r!(n-r)!), we can calculate the probability as (14*13*12*11)/(4*3*2*1*10^5) which simplifies to 0.5148 or 51.48%.