in this question paranthases are correct,just in this 10 has power 4.please i neede this early.its frm combination and permutation of probability.
10^4C(25,5)
____________
7!P(30,4)
To solve this question, we need to understand the concepts of combinations, permutations, and probability.
First, let's break down the expression:
10^4C(25,5) / 7!P(30,4)
1. Combinations (C):
The notation C(n, r) represents the number of ways to choose r items from a set of n items without considering the order. In this case, we have 25 items, and we want to choose 5 of them. So, C(25, 5) represents the number of combinations of 25 items taken 5 at a time.
2. Permutations (P):
The notation P(n, r) represents the number of ways to arrange r items from a set of n items while considering the order. In this case, we have 30 items, and we want to arrange 4 of them. So, P(30, 4) represents the number of permutations of 30 items taken 4 at a time.
3. Exponents:
The notation a^b represents a raised to the power of b. In this case, we have 10 raised to the power of 4, which means we have 10 * 10 * 10 * 10.
Now let's calculate the expression step by step:
Step 1: Calculate the combination 25C5.
This can be calculated using the formula: C(n, r) = n! / (r! * (n-r)!).
So, 25C5 = 25! / (5! * (25-5)!) = 25! / (5! * 20!).
Step 2: Calculate the permutation 30P4.
This can be calculated using the formula: P(n, r) = n! / (n-r)!.
So, 30P4 = 30! / (30-4)! = 30! / 26!.
Step 3: Calculate 10^4.
10^4 = 10 * 10 * 10 * 10 = 10,000.
Step 4: Calculate 7!.
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040.
Now, substitute the values into the expression:
Final result = (10,000 * 25C5) / (7! * 30P4)
= (10,000 * (25! / (5! * 20!))) / (5,040 * 30!)
To calculate the final result, you need to compute the values of 25!, 20!, and 30! and carry out the division accordingly.
Please note that the calculation of factorials and the final result may involve large numbers. Consider using a calculator or a computer program capable of handling such calculations precisely.