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Chapter 13: Q. 23 (page 855)

List all the ordered arrangements of 5 objects a,b,c,d, and echoosing 3 at a time without repetition. What isP(5,3)?

Short Answer

Expert verified

The list of ordered arrangements is:

abc,abd,abe,acb,acd,ace,adb,adc,ade,aeb,aec,aed,bac,bad,bae,bca,bcd,bce,bda,bdc,bde,bea,bec,bed,cab,cad,cae,cba,cbd,cbe,cda,cdb,cde,cea,ceb,ced,dab,dac,dae,dba,dbc,dbe,dca,dcb,dce,dea,deb,dec,eab,eac,ead,eba,ebc,ebd,eca,ecb,ecd,eda,edb,edc.

The value of the permutation is 60.

Step by step solution

01

Step 1. Given information.

3 objects are chosen from 5 objects a,b,c,d, and eat a time without repetition.

The given permutation is P(5,3).

02

Step 2. Determine the list of ordered arrangements.

The list of ordered arrangements is:

abc,abd,abe,acb,acd,ace,adb,adc,ade,aeb,aec,aed,bac,bad,bae,bca,bcd,bce,bda,bdc,bde,bea,bec,bed,cab,cad,cae,cba,cbd,cbe,cda,cdb,cde,cea,ceb,ced,dab,dac,dae,dba,dbc,dbe,dca,dcb,dce,dea,deb,dec,eab,eac,ead,eba,ebc,ebd,eca,ecb,ecd,eda,edb,edc.

03

Step 3. Determine the value of permutation.

We know that,

P(n,r)=n!(n-r)!

Using the above formula, we get

localid="1647083212967" P(5,3)=5!(5-3)!=5!2!=5脳4脳3脳2!2!=60

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