Evaluate 11C7 and 9P3
To evaluate 11C7, we can use the combination formula:
11C7 = 11! / (7!(11-7)! )
= 11! / (7!4! )
= (11 * 10 * 9 * 8 * 7!) / (7! * 4 * 3 * 2 * 1)
= (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1)
= 330
To evaluate 9P3, we can use the permutation formula:
9P3 = 9! / (9-3)!
= 9! / 6!
= (9 * 8 * 7 * 6!) / 6!
= (9 * 8 * 7)
= 504
To evaluate 11C7, we need to calculate the number of combinations of 11 objects taken 7 at a time.
The formula for combinations is given by: nCk = n! / (k!(n-k)!), where n! denotes the factorial of n.
Using this formula, we can find 11C7 as follows:
11C7 = 11! / (7!(11-7)!)
= 11! / (7! * 4!)
= (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1)
= (7920) / (24)
= 330
Therefore, 11C7 is equal to 330.
To evaluate 9P3, we need to calculate the number of permutations of 9 objects taken 3 at a time.
The formula for permutations is given by: nPk = n! / (n-k)!, where n! denotes the factorial of n.
Using this formula, we can find 9P3 as follows:
9P3 = 9! / (9-3)!
= 9! / 6!
= (9 * 8 * 7) / (3 * 2 * 1)
= (504) / (6)
= 84
Therefore, 9P3 is equal to 84.