Question

2. How many ways can seven colored beads be arranged (a) on a straight wire, (b) on a circular necklace? (Hint: think about the kinds of manipulations that would or would not result in a “distinguishable” configuration of beads) 3. How many distinguishable five-card poker hands are possible? Note that reordering the cards in your hand does not change the nature of the hand.

3. How many distinguishable five-card poker hands are possible? Note that reordering the cards in your hand does not change the nature of the hand.

6. A firm has to choose seven people from its R and D team of ten to send to a conference on computer systems. How many ways are there of doing this (a) when there are no restrictions? (b) when two of the team are so indispensable that only one of them can be permitted to go? (c) when it is essential that a certain member of the team goes?

Answer 1

How many ways can seven colored beads be arranged

(a) on a straight wire,

n!

7!=5040 ways

(b) on a circular necklace?

In case of circular permutation, n things can be arranged in (n-1)! ways.

Now, in a necklace, the clockwise and anticlockwise arrangements are the same as it is symmetrical.

So,TOTAL ARRANGEMENTS = [(n−1)!/2]

Here we have 7 beads in a necklace.

So, no. of arrangements is [(7−1)!/2]=[(6!/2] =360 ways

3.How many distinguishable five-card poker hands are possible? Note that reordering the cards in your hand does not change the nature of the hand.

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6.A firm has to choose seven people from its R and D team of ten to send to a conference on computer systems. How many ways are there of doing this

(a) when there are no restrictions?

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(b) when two of the team are so indispensable that only one of them can be permitted to go?

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(c) when it is essential that a certain member of the team goes?

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