How many integers between 100 and 999, inclusive, have all their digits odd and distinct?



Answer to a math question How many integers between 100 and 999, inclusive, have all their digits odd and distinct?

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Para encontrar o número de inteiros entre 100 e 999 (inclusive) onde todos os dígitos são ímpares e distintos, precisamos considerar as combinações possíveis. 1. O algarismo das centenas pode ser qualquer algarismo ímpar de 1 a 9 (1, 3, 5, 7 ou 9). 2. O algarismo das dezenas pode ser qualquer algarismo ímpar, exceto aquele já escolhido para o algarismo das centenas. 3. O algarismo das unidades pode ser qualquer algarismo ímpar, exceto os já escolhidos para os algarismos das centenas e das dezenas. Portanto, o número de inteiros que atendem a essas condições é o produto do número de escolhas para cada dígito: 1. Existem 5 opções para o algarismo das centenas (1, 3, 5, 7, 9). 2. Existem 4 opções para o algarismo das dezenas (excluindo a já escolhida para o algarismo das centenas). 3. Existem 3 opções para o algarismo das unidades (excluindo as já escolhidas para os algarismos das centenas e dezenas). Portanto, o número total de inteiros que atendem às condições é: \[ 5 \vezes 4 \vezes 3 = 60 \] Portanto, existem 60 números inteiros entre 100 e 999 (inclusive) onde todos os dígitos são ímpares e distintos.

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