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Multiplication of Matrices

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Question

Find the total number of selections of A + B + C + D objects where A are alike (of $1^{s t}$ kind), B are alike (of $2^{n d}$ kind), C are alike (of $3^{r d}$ kind) and D are alike (of $4^{t h}$ kind).

A + B + C + D

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(A +1) (B + 1) (C +1) (D+1)

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(A +1) (B + 1) (C +1) (D+1) - 1

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Solution

The correct option is B
(A +1) (B + 1) (C +1) (D+1)

The total number of selections of A + B + C + D objects where A are alike (of $1^{s t}$ kind), B are alike (of $2^{n d}$ kind), C are alike (of $3^{r d}$ kind) and D are alike (of $4^{t h}$ kind)

Number of ways of selecting A alike objects = Selecting zero of $1^{s t}$ kind of objects or Selecting one of $1^{s t}$ kind of objects or Selecting two of $1^{s t}$ kind of

objects........ Selecting (A- 1) of $1^{s t}$ kind of objects or Selecting all A objects of $1^{s t}$ kind of objects

Number of ways of selecting A alike objects = (A + 1) ways

Similarly,

Number of ways of selecting B alike objects = (B + 1) ways

Number of ways of selecting C alike objects = (C + 1) ways

Number of ways of selecting D alike objects = (D + 1) ways

Total number of selections of A + B + C + D objects

= (A +1) (B + 1)(C +1) (D+1)

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Similar questions

Find the total number of selections of A + B + C + D objects where A are alike (of one kind), B are alike (of second kind), C are alike (of third kind) and D are alike (of fourth kind) if he has to select at least one of each kind of object.

Q. I: The total number of ways in which a selection (one or more) can be made of

p + q + r

things of which

p

are alike,

q

are alike,

r

are alike is

(p + 1) (q + 1) (r + 1) - 1

II: The number of permutations of n things taken together when

p

of the things are alike of one kind,

q

of them alike of a second kind,

r

of them alike of a third kind and the rest all different is

\frac{n!}{p! q! r! 3!}

Which of the above statements is true?

a

\frac{1}{b}

c

and

\frac{1}{d}

are in proportion. Then,

Q. If

A, B

and

C

are invertible matrices and

B A C = I,

the value of

A

Q. There are

13

letters of

8

different sorts

I, I, I, S, S, T, T, L, L, A, O, N, D

. In finding groups of

4

, how many permutations can be made if following are the possibilities to be considered? If

2

are alike of one kind and

2

are alike of other kind.

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Find the total number of selections of A + B + C + D objects where A are alike (of 1stkind), B are alike (of 2nd kind), C are alike (of 3rd kind) and D are alike (of 4th kind).

Find the total number of selections of A + B + C + D objects where A are alike (of $1^{s t}$ kind), B are alike (of $2^{n d}$ kind), C are alike (of $3^{r d}$ kind) and D are alike (of $4^{t h}$ kind).