Generate rows of Pascal's Triangle, essential for binomial expansion and combinatorics. Select the number of rows to explore Pascal's Triangle for pattern recognition and binomial applications.
The value at row 4, column 2 is found using the binomial coefficient formula: C(n, k) = n! / (k!(n - k)!)
For n = 4 and k = 2:
C(4, 2) = 4! / (2!(4 - 2)!) = 24 / (2 × 2) = 6
Answer: 6
C(6, 3) = 6! / (3!(6 - 3)!) = 720 / (6 × 6) = 20
Answer: 20
The first element in each row of Pascal's Triangle is always 1. So, C(7, 0) = 1.
Answer: 1
C(8, 4) = 8! / (4!(8 - 4)!) = 40320 / (24 × 24) = 70
Answer: 70
C(5, 1) = 5! / (1!(5 - 1)!) = 120 / (1 × 24) = 5
Answer: 5
C(9, 2) = 9! / (2!(9 - 2)!) = 362880 / (2 × 5040) = 36
Answer: 36
C(10, 5) = 10! / (5!(10 - 5)!) = 3628800 / (120 × 120) = 252
Answer: 252
The last element in each row is always 1. So, C(3, 3) = 1.
Answer: 1
C(6, 2) = 6! / (2!(6 - 2)!) = 720 / (2 × 24) = 15
Answer: 15
C(11, 3) = 11! / (3!(11 - 3)!) = 39916800 / (6 × 40320) = 165
Answer: 165