Final answer:
To find 10C4 times 4C2, we calculate the combinations 10C4 and 4C2. Multiplying these combinations gives the solution 1260.
Step-by-step explanation:
To find the solution to 10C4 times 4C2, we need to calculate the combination of 10 objects taken 4 at a time (10C4) and multiply it by the combination of 4 objects taken 2 at a time (4C2).
The formula for combination is nCr = n! / (r!(n-r)!), where n is the total number of objects and r is the number of objects taken at a time.
Substituting the values, we have:
10C4 = 10! / (4!(10-4)!) = 10! / (4!6!)
4C2 = 4! / (2!(4-2)!) = 4! / (2!2!)
Multiplying these two combinations, we get:
10C4 * 4C2 = (10! / (4!6!)) * (4! / (2!2!))
Simplifying the equation, we can cancel out the factorial terms:
10C4 * 4C2 = (10*9*8*7) / (4*3*2*1) * (4*3) / (2*1) = 210 * 6 = 1260.