A five digit security code consists five digits chosen from: the 26 uppercase le

Question

A five digit security code consists five digits chosen from: the 26 uppercase letters from the alphabet, the 26 lowercase letters from the alphabet, the set of digits {0, , 9 … } , and the keyboard symbols, {!,@, #,$,%,&,*, , ,? < > } .

a. How many five digit security codes are there?

b. How many five digit security codes which consist of at least one upper case and one lower case letter are there?

c. How many five digit security codes that do not contain a digit chosen from {0, , 9 … } are there?

Explanation / Answer

UpperCase Letters = 26
lower Case Letters = 26
DIgits ( 0 - 9 ) = 10
Keyboard Symbols {!,@, #,$,%,&,*, , ,? < > } = 11

Total number of choices available to choose from are 26+26 +10+11 = 73
  

a )     For first place we can select any thing from these 73 choices and as there is no restriction , it applies the same for other 4 places .... Thus the total five digit security codes combinations available are
       73 * 73 *73 * 73 * 73 = 2073071593

b) For two places we have restriction of Lower and upper case and rest three can be anything thus it will be

      26 * 26 * 73 * 73 * 73 = 262975492

c) As the restriction is for only Digits , we left with chocies of 73-10 = 63

    63 * 63 * 63 * 63 * 63 = 992436543

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.