Solve:
6c3
A.120
B.720
C.20
D.240
How many ways can you choose 3 dishes from a menu of 8?
A.24
B.336
C.144
D.56
Solve 6p4
A.240
B.720
C.20
D.360
To solve 6C3, which represents the number of ways to choose 3 items from a set of 6, we can use the formula for combinations:
nCr = n! / (r! * (n - r)!)
In this case, n = 6 and r = 3:
6C3 = 6! / (3! * (6 - 3)!)
= (6 * 5 * 4) / (3 * 2 * 1)
= 20
Therefore, the answer is C.20.
To solve the question "How many ways can you choose 3 dishes from a menu of 8?", we can use the same formula for combinations:
8C3 = 8! / (3! * (8 - 3)!)
= (8 * 7 * 6) / (3 * 2 * 1)
= 56
Therefore, the answer is D.56.
Now let's solve 6P4, which represents the number of permutations of 6 objects taken 4 at a time. The formula for permutations is:
nPn = n!
In this case, n = 6:
6P4 = 6!
= 6 * 5 * 4 * 3 * 2 * 1
= 720
Therefore, the answer is B.720.
To solve 6c3, we use the combination formula:
nCr = n! / (r!(n-r)!)
Plugging in the values, we have:
6c3 = 6! / (3!(6-3)!)
= 6! / (3!3!)
= (6 × 5 × 4) / (3 × 2 × 1)
= 20
Therefore, the answer is C.20.
To calculate how many ways you can choose 3 dishes from a menu of 8, we also use the combination formula:
nCr = n! / (r!(n-r)!)
Plugging in the values, we have:
8c3 = 8! / (3!(8-3)!)
= 8! / (3!5!)
= (8 × 7 × 6) / (3 × 2 × 1)
= 56
Therefore, the answer is D.56.
To solve 6p4, we use the permutation formula:
nP r = n! / (n-r)!
Plugging in the values, we have:
6p4 = 6! / (6-4)!
= 6! / 2!
= (6 × 5 × 4 × 3) / (2 × 1)
= 360
Therefore, the answer is D.360.
you should know these w definitions
nCr = n!/( r!(n-r)! )
nPr = n!/(n-r)!
6C3 = 6!/(3!3!) = 20
6P4 = 6!/2! = 360
On most scientific calculators both of these functions are built-in
on mine they are found below the 5 - key and the 6-key
to do 6C3
enter
6
2ndF
5
3
=
to get 20
How many ways can you choose 3 dishes from a menu of 8?
8C3 = 56