The number of different pairs of words $$\left( {\square \square \square \square ,\square \square \square } \right)$$ that can be made with the letters of the word STATICS is
A.
828
B.
1260
C.
396
D.
None of these
Answer :
1260
Solution :
From every arrangement of 7 letters we get a pair by putting a sign (,) after the four letters from the left.
∴ the required number of pairs $$ = \frac{{7!}}{{2!\,2!}}.$$
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
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is