The number of different matrices that can be formed with elements 0, 1, 2, or 3, each matrix having 4 elements, is
A.
$$3 \times {2^4}$$
B.
$$2 \times {4^4}$$
C.
$$3 \times {4^4}$$
D.
None of these
Answer :
$$3 \times {4^4}$$
Solution :
The matrix will be of the order $$4 \times 1$$ or $$1 \times 4$$ or $$2 \times 2.$$
For each order, the number of different matrices
= the number of ways to fill four places by 0, 1, 2, 3
$$ = 4 \times 4 \times 4 \times 4.$$
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are
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