Permutation

Identify whether each situation illustrates permutation or not.

Picking 2 fruits from a basket of 10 different fruits.

• PERMUTATION

• NOT PERMUTATION

What does ₁₀P₅ mean?

• Permutations with 5 choices and 10 positions
• Permutations with 10 choices and 5 positions
• Permutations with 5 numbers and 10 operations
• Permutations with 5 hot dogs and 10 drinks

Use a Calculator. to find the value of

8!

Answer explanation

8! is the same as 8 x 7 x 6 x .. x 1

n P n = ____

• n C n

• n!

• n P r

• r!

Answer explanation

Example 3 P 3 is 6 = 3!

Find out the number of ways 7 boys can be arranged in a line.

Answer explanation

Since you need to arrange 7

entities in a row, hence

7! = 7 x 6 x ... x 1

Find the number of ways the letters in the word ORANGE may be rearranged with no restriction.

Answer explanation

Since you need to arrange 6

entities in a row, hence

6! = 6 x ... x 1

Find the number of ways the letters in the word ORANGE may be rearranged if only 3 letters can be used.

Answer explanation

Since you need to arrange 6

entities in a row with only 3 entities to be used, hence

6!/ (6-3)!

Use the trial and error method to find the value of n if

n P 4 = 5040

Answer explanation

9 P 4 = 3024 X

Since 9 gives a smaller value than 5040, we need to use a higher n value.

Find the value if n P 3 = n P 2, find the value of n.

Answer explanation

Use trial and error to test starting from 1.

Alternatively you can use the n P r formula to work it out.

A 5-digit password is to created using the digits from 0 to 9.

If a computer system needs 0.1s to test each random number until the final password is found, how long will it take ( in seconds) the system to test all possible permutation?

Answer explanation

10^5 = all possible permutation

1 password takes 0.1s to test so 10^5 passwords will take ........ to test.