A digital locker has an alpha-numeric (it can have both digits and letters) passcode of length 5. Class 8

A digital locker has an alpha-numeric (it can have both digits and letters) passcode of length 5. Class 8

Question 1.

A digital locker has an alpha-numeric (it can have both digits and letters) passcode of length 5. Some example codes are G89P0, 38098, BRJKW, and 003AZ. How many such codes are possible?

Solution:

Sum of letters and digits = 26 + 10 = 36.

So, for a passcode of length 5, number of codes possible = 36 × 36 × 36 × 36 × 36 = 36⁵.

Question 2.

The worldwide population of sheep (2024) is about 109, and that of goats is also 'about the same. What is the total population of sheep and goats?

(i) 20⁹

(ii) 10¹¹

(iii) 10¹⁰

(iv) 10¹⁸

(v) 2 × 10⁹

(vi) 10⁹ + 10⁹

Solution:

(v) 2 × 10⁹ and

(vi) 10⁹ + 10⁹