Question

How many matrices can be obtained by using one or more numbers from four given numbers?

Options

• 76

• 148

• 124

• 82

Answer 1

148

Explanation:

Taking any four digits as 1, 2, 3, 4

No. of matrices = taking either one digit or

two digits or three digits or four digits

Taking one digit, no. of matrices = ⁴C₁

Taking two digits, no. of matrices = ⁴C₂ × 2! × 2*

(*because they are either in row matrix or column matrix)

Taking three digits, no. of matrices = ⁴C₃ × 3! × 2*

(*because they are either in row matrix or column matrix)

Taking four digits, no. of matrices

(** because they are either 4 × 1 or 1 × 4 or 2 × 2 matrices).

∴ Total no. of matrices = ⁴C₁ + ⁴C₂ × 2! × 2 + ⁴C₃ × 3! × 2 + ⁴C₄  × 4! × 3

= `4 + (4!)/(2! xx 2!) xx 2! xx 2 + (4!)/(1! xx 3!) xx 3! xx 2 + 4! xx 3`

= 4 + 24 + 48 + 72

= 4 + 144

= 148