How many different car license plates can be constructed if license contains 2 l

Question

How many different car license plates can be constructed if license contains 2 letters followed by 4 digits: a. If repetitions are not allowed b. If repetitions are allowed c. If letters cannot repeat but numbers can In how many ways can we select a chairperson, vice - chairperson and a president from the group of 25 people? Determine how many strings can be formed by ordering the letters ABCDEFGHIJKL so the string starts with the substring 'ABC' or ends with the substring 'EDF' or both? A Chess Club has ten members. In how many ways: a. Can all then members line up for a picture? b. Can the club president and a secretary be selected? c. Can the club choose four members to attend a regional tournament with no regard to order?

Explanation / Answer

20)for repetitions are allowed

number of ways =262*104 =5760000

repetitions are not allowed =26*25*10*9*8*7=3276000

letters cannot but number can =26*25*104 =6500000

21)Number of ways =(25!/(22!) =13800

22) number with ABC in start =9! =362880

number with EDF in end =9! =362880

number with ABC in start and EDF in end =6! =720

hence total numebr =362880+362880-720=725040

23)total numebr of wways trhey can line up =10! =3628800

number of ways president and secretary can be selected =10!/8! =90

chooses 4 memberes =choose(10,4)=10!/(4!*6!) =210

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