**Permutation with replacement**

In the previous explanation, permutation which we got is permutation where an objects is only used one time, or this is called permutation without replacement. Sometimes the objects provided can be used many times, and in this thing the permutation which is got is called permutation with replacement or permutation with recovery.

Suppose in forming the numeral which contain of 2 digits, which is taken from 3 numerals are provided, which are: 1, 2, and 3. If the numeral which are used can be repeated or is replaced after used before, we’ll get the numeral, which are:

The number of permutation is equal to 9. Pay attention that 9=3

^{2}. This permutation is called permutation with recovery or permutation with replacement or different arrangements with recovery.

If *k* of elements are taken from m of elements that are provided, where the element provided can be chosen repeatedly (permutation with recovery), then the number of permutation =*m*^{k}.

**Example 13**:

a. Determine the number of numbers ehich is consist of 3 numerals which can be formed from the numerals: 1,

b. Determine the number of the permutation (the arrangement that is different) which are possible in the tossing of a coin for 3 times.

Answer:

a. Four numerals are provided, taken 3 numerals. The number of number which can be formed =4

^{3}=64.

b. There are two sides of coin which are numeral (N) and image (E). The coin is tossed for 3 times. The number of permutation =2

^{3}=8. The permutation are:

**Exercise Competency Test 13**

1. A coin is tossed 4 times. The number of different arrangements as the result of the tossing is equal to …

A. 16 B. 14 C. 8 D. 6 E. 4

Answer: Explanation:

A coin has two sides.

^{4}=16

2. Mr. Kardi has bag which can be loked by secret code. The code contains three numerals. The numeral which is used are from 0 until 9. The number of code which is possible which he make in his bag is equal to ….

A. 4^{10} B. 3^{10} C. 2^{10} D. 10^{3} E. 9^{3}

Answer: D, Explanation:

*n*(nums)=10

=10

^{3}

3. A programmer wants to make a password which contain of 4 numerals. If the first numeral is always started by numeral 1 and the numerals are used can be repeated, then the number of passwords which can be made =…

A. 4^{10} B. 3^{10} C. 10^{4} D. 10^{3} E. 10^{2}

Answer: B, Explanation:

*n*(nums)=10

(4-1)

^{10}=3

^{10}

4. In Jakarta, generally the license plate of taxi is consist of one letter which is B and it is followed by 4 digits and two letters. The last letter always uses letter X, and first digit always uses numerals: 1 or 2. For example B 1234 KX. So, the number of license plate of taxi which can be made in Jakarta =…

A. 520000 B. 260000 C. 52000 D. 26000 E. 520

Answer: C Explanation: