Question

The Reserve Bank of India prints currency notes in denominations of Five rupees, Ten rupees, Twenty rupees, Fifty rupees, One hundred rupees, Five hundred rupees and One hundred rupees. In how many ways can it display in a set order ten currency notes not necessarily of different denominations? How many of these will have currency notes of all denominations?

• A. $7^{10};{(}^{10}{C}_7)7^3$
  
• B. $7^{10};{(}^{10}{C}_7)7!\times 7^7$
  
• C. $7^{10};{(}^{10}{C}_7)7!\times 7^3$
  
• D. None of these

Answer 1

The correct option is C $7^{10};{(}^{10}{C}_7)7!\times 7^3$

for each currency note there will be $7$ possibilities

$⟹$for 10 currency notes no. of possibilities are $7^{10}$

in the 10 currency notes ,all denominations must be there

$⟹$we must select $7$ notes in the $10$ notes which can be done in ${}^{10}{C}_7$ ways and we have to arrange all the 10 notes $⟹{(}^{10}{C}_7)7!\times 7^3$