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1

### IIT-JEE 1982

The value of the expression $$\,{}^{47}{C_4} + \sum\limits_{j = 1}^5 {^{52 - j}\,{C_3}}$$ is equal to
A
$${}^{47}{C_5}$$
B
$${}^{52}{C_5}$$
C
$${}^{52}{C_4}$$
D
none of these
2

### IIT-JEE 1982

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
A
$${}^6{C_3} \times {}^4{C_2}$$
B
$${}^4{P_2} \times {}^4{P_3}$$
C
$${}^4{C_2} \times {}^4{P_3}$$
D
none of these
3

### IIT-JEE 1982

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the numbers of words which have at least one letter repeated are
A
69760
B
30240
C
99748
D
none of these
4

### IIT-JEE 1979

$${}^n{C_{r - 1}} = 36,{}^n{C_r} = 84\,\,and\,\,{}^n{C_{r + 1}} = 126$$, then r is :
A
1
B
2
C
3
D
None of these.

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