Read the statements given below carefully.
(A) Five friends P, Q, R, S and T are to sit in a row of 5 chairs. The number of ways in which they can sit so that P and Q occupy the two end chairs is 12.
(B) The number of 3-digit numbers whose digits are all odd, when the repetition of digits is allowed, is 60.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Only (A)
Places with a condition are filled first, then the rest; the numbers of choices are multiplied. With repetition allowed, every place can take any allowed digit again.
(A) The number of ways in which they can sit so that P and Q occupy the two end chairs is 12 Correct.
P and Q take the two end chairs in \(2!=2\) ways (P left and Q right, or the other way)
R, S and T fill the 3 middle chairs in \(3!=6\) ways
Ways \(=2\times6=12\)
(B) The number of 3-digit numbers whose digits are all odd, when the repetition of digits is allowed, is 60 Incorrect.
Odd digits: 1, 3, 5, 7, 9, that is 5 choices for each place
Numbers \(=5\times5\times5=125\), not 60 (60 is \(5\times4\times3\), the count without repetition)