G Tewani Solutions for Chapter: Permutation and Combination, Exercise 2: Archives

From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is

There are two urns. Urn $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urn, two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from $10$ white, $9$ green and $7$ black balls is

If $z$ is a complex number of unit modulus and argument $\theta ,$ then $arg\left(\frac{1+z}{1+\overline{z}}\right)$ equals

If $z$ a complex number such that $\left|z\right|\ge 2$, then the minimum value of $\left|z+\frac{1}{2}\right|$

The number of integers greater than $6000$ that can be formed, using the digits $3, 5, 6, 7$ and $8$ without repetition, is

Six cards and six envelopes are numbered $1, 2, 3, 4, 5, 6$ and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered $1$ is always placed in envelope numbered $2$. Then the number of ways it can be done is

A debate club consists of $6$ giris and $4$ boys. A team of $4$ members is to be selected from this club including the selection of a captain (from among these $4$ members) for the team. If the team has to include at most one boy. Then the number of ways of selecting the team is